Characterizations of discrete distributions by a conditional distribution and a regression function

Summary The bivariate distribution of (X, Y), whereX andY are non-negative integer-valued random variables, is characterized by the conditional distribution ofY givenX=x and a consistent regression function ofX onY. This is achieved when the conditional distribution is one of the distributions: a) binomial, Poisson, Pascal or b) a right translation of these. In a) the conditional distribution ofY is anx-fold convolution of another random variable independent ofX so thatY is a generalized distribution. A main feature of these characterizations is that their proof does not depent on the specific form of the regression function. It is also indicated how these results can be used for good-ness-of-fit purposes.     

Complete Oxidation of Methane over Palladium Supported on Alumina Modified with Calcium,Lanthanum,and Cerium Ions

The activity and thermal stability of Pd/Al_2O_3 and Pd/(Al_2O_3 MO_x)(M=Ca,La,Ce) palladium catalysts in the reaction of complete oxidation of methane are presented in this study.The catalyst supports were prepared by sol-gel method and they were dried either conventionally or with supercritical carbon dioxide.Then they were impregnated with palladium nitrate solution.The catalysts with unmodified alumina had a high surface area.The activity and thermal stability of the alumina- supported catalyst was also very high.The introduction of calcium,lanthanum,or cerium oxide into alumina support caused a decrease of the surface area in the way dependent on the support precursor drying method.These modifiers decreased the activity of palladium catalysts,and they required higher temperatures for the complete oxidation of methane than unmodified Pd/Al_2O_3.The improvement of the palladium activity by lanthanum and cerium support modifier was observed only at low temperatures of the reaction.     

Ultrafast photofragmentation dynamics of molecular iodine driven with timed XUV and near-infrared light pulses

Photofragmentation dynamics of molecular iodine was studied as a response to the joint illumination with femtosecond 800 nm near-infrared and 13 nm extreme ultraviolet (XUV) pulses delivered by the free-electron laser facility FLASH. The interaction of the molecular target with two light pulses of different wavelengths but comparable pulse energy elucidates a complex intertwined electronic and nuclear dynamics. To follow distinct pathways out of a multitude of reaction channels, the recoil of created ionic fragments is analyzed. The delayed XUV pulse provides a way of following molecular photodissociation of I(2) with a characteristic time-constant of (55 ± 10) fs after the laser-induced formation of antibonding states. A preceding XUV pulse, on the other hand, preferably creates a 4d(-1) inner-shell vacancy followed by the fast Auger cascade with a revealed characteristic time constant τ(A2)=(23±11) fs for the second Auger decay transition. Some fraction of molecular cationic states undergoes subsequent Coulomb explosion, and the evolution of the launched molecular wave packet on the repulsive Coulomb potential was accessed by the laser-induced postionization. A further unexpected photofragmentation channel, which relies on the collective action of XUV and laser fields, is attributed to a laser-promoted charge transfer transition in the exploding molecule.     

Synthesis of transparent silica aerogels using tetraalkylammonium fluoride catalysts

Tetraalkylammonium fluoride salts have been employed as catalysts for the synthesis of silica aerogels by a two-step, sol–gel method. Aerogel materials were characterized by N₂ physisorption and SEM. The effect of the type of catalyst on the optical transparency of obtained aerogels has been examined. It has been found that such compounds allow the synthesis of silica aerogels with the highest optical transmittance ever reported for such materials. The optimal catalysts are tetrabutyl and tetraoctyl ammonium fluoride, with which aerogels with transparency as high as 96% and extinction coefficient as low as 3.5 m⁻¹ can be prepared.     

Wave-function mapping of InAs quantum dots by scanning tunneling spectroscopy

Scanning tunneling spectroscopy is used to investigate the single-electron states and the corresponding squared wave functions of single and freestanding strain-induced InAs quantum dots grown on GaAs(001). Several peaks are found in dI/dV curves, which belong to different single-electron states. Spatially resolved dI/dV images reveal (000), (100), (010), (200), and (300) states, where the numbers describe the number of nodes in [11;0], [110], and [001] directions, respectively. The total number and energetic sequence of states is different for different dots. Interestingly, the (010) state is often missing, even when (200) and (300) states are present. We interpret this anisotropy in electronic structure as a consequence of the shape asymmetry of the dots.     

On upper bounds for the variance of functions of random variables

The upper bounds for the variance of a function g of a random variable X obtained in Cacoullos (1982) (for short CP) are improved in the case μ = E(X) ≠ 0. A main feature of these bounds is that they involve the second moment of the derivative or the difference of g. A multivariate extension for functions of independent random variables is also given.     

Characterizations of mixtures of discrete distributions by a regression point

Given that the conditional distribution p_s(y|x) of Y, given X = x is an x-fold convolution of a nonnegative integer-valued r.v. ξ for every s= P[ξ = 0] > 0, the distribution of X, hence also of Y, is characterized by the regression point m(0) = E[X|Y = 0]. An infinite variety of generalized distributions (of Y) can be characterized by arbitrarily varying the distribution of X.     

Complex networks and banking systems supervision

Comprehensive and thorough supervision of all banking institutions under a Central Bank’s regulatory control has become necessary as recent banking crises show. Promptly identifying bank distress and contagion issues is of great importance to the regulators. This paper proposes a methodology that can be used additionally to the standard methods of bank supervision or the new ones proposed to be implemented. By this, one can reveal the degree of banks’ connectedness and thus identify “core” instead of just “big” banks. Core banks are central in the network in the sense that they are shown to be crucial for network supervision. Core banks can be used as gauges of bank distress over a sub-network and promptly raise a red flag so that the central bank can effectively and swiftly focus on the corresponding neighborhood of financial institutions. In this paper we demonstrate the proposed scheme using as an example the asset returns variable. The method may and should be used with alternative variables as well.