P\'olya number of continuous-time quantum walks

We propose a definition for the P\'olya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their P\'olya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.Comment: 8 pages, no figures. Accepted for publication in Physical Review

Establishment and Early Operations of the State Audit Office of Hungary

Re-established in 1867 by the Austro-Hungarian Compromise, parliamentarism institutionalised the powers of the legis-lature to exercise control over the government in Hungary as well, and Parliament established the State Audit Office to carry out the duty of economic control. However, Act XVIII of 1870 codifying the State Audit Office contained ambiguous provisions on its legal status, specifying only arithmetic control as its task, as a result of which the operations of the Office, from the beginning to its dis-continuation, were described in contradictory terms

Stochastic integration based on simple, symmetric random walks

A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s. uniform convergence on compacts. In particular, it gives a.s. convergence for the stochastic integral of a finite variation function of the integrator, which is not c\`adl\`ag in general.Comment: 16 pages, some typos correcte

A sajtószabadság ügye a kiegyezés utáni évek Magyarországán = The Freedom of the Press in Hungary After the Compromise of 1867

A sajtószabadságot 1848 márciusa hozta el Magyarországra. Pesten a márciusi ifjak a felkelő polgárok segítségével szakítottak a cenzúra több évszázados gyakorlatával, Pozsonyban pedig az utolsó rendi gyűlés liberális nemessége törvényt fogadott el, amely kimondta: „Gondolatait sajtó útján mindenki szabadon közölheti és szabadon terjesztheti.” A szabadságharc leverésével bő másfél évtizedre elérhetetlen távolságba került a véleményszabadság a nemzet legjobbjai számára. Bécs és Pest, valamint a Habsburg dinasztia 1867-es kiegyezése az alkotmányosság helyreállításával a nyomtatott betű újbóli felszabadítását jelentette. A Szemere Bertalan tollából származó 48-as törvényt ismét hatályba léptették, s ez szimbolikus üzenetet is hordozott: a nemzet ragaszkodását Kossuth, Széchenyi, Deák és a többiek eszményeihez. A sajtó felszabadításával, majd két esztendővel később a hírlapokra nehezedő anyagi terhek csökkentésével Andrássy Gyula és kormánya ország-világ előtt bizonyította a liberális eszmék és intézmények iránti elkötelezettségét

High glass forming ability correlated with microstructure and hydrogen storage properties of a Mg-Cu-Ag-Y glass

Thermal characterization of an as-cast Mg54Cu28Ag7Y11 bulk metallic glass revealed that this alloy exhibits excellent glass forming ability. High-resolution X-ray diffraction study and transmission electron microscopy show that heating and isothermal annealing treatment results in the nucleation of nanocrystals of several phases. The average size of these nanocrystals (~15-20 nm) only slightly varies with prolonged annealing, only their volume fraction increases. High-pressure calorimetry experiments indicate that the as-cast fully amorphous alloy exhibits the largest enthalpy of hydrogen desorption, compared to partially and fully crystallized states. Since the fully crystallized alloy does not desorb hydrogen, it is assumed that hydrogen storage capacity correlates only with the crystalline volume fraction of the partially crystallized Mg54Cu28Ag7Y11 BMG and additional parameters (crystalline phase selection, crystallite size, average matrix concentration) do not play a significant role

Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probabilit