Potential Theory of Geometric Stable Processes

In this paper we study the potential theory of symmetric geometric stable processes by realizing them as subordinate Brownian motions with geometric stable subordinators. More precisely, we establish the asymptotic behaviors of the Green function and the Lévy density of symmetric geometric stable processes. The asymptotics of these functions near zero exhibit features that are very different from the ones for stable processes. The Green function behaves near zero as 1/(|x|^d log ²|x|), while the Lévy density behaves like 1/|x|^d. We also study the asymptotic behaviors of the Green function and Lévy density of subordinate Brownian motions with iterated geometric stable subordinators. As an application, we establish estimates on the capacity of small balls for these processes, as well as mean exit time estimates from small balls and a Harnack inequality for these processes. The research of this author is supported in part by MZT grant 0037118 of the Republic of Croatia and in part by a joint US-Croatia grant INT 0302167. The research of this author is supported in part by a joint US-Croatia grant INT 0302167. The research of this author is supported in part by MZT grant 0037107 of the Republic of Croatia and in part by a joint US-Croatia grant INT 0302167.     

A characterization ofh-Brownian motion by its exit distributions

Summary LetX ^h be anh-Brownian motion in the unit ballDR ^d withh harmonic, such that the representing measure ofh is not singular with respect to the surface measure on D. IfY is a continuous strong Markov process inD with the same killing distributions asX ^h , thenY is a time change ofX ^h . Similar results hold in simply connected domains inC provided with either the Martin or the Euclidean boundary.     

Synthesis and DFT Defined trans (O5O6) Molecular Structure of Cs[Fe(1,3- pddadp )] · 2H2O. Strain Analysis and Spectral Assignment of the Complex

An iron(III) complex with the hexadentate ligand 1,3-propanediamine-N,N′-diacetate-N,N′-di-3-propionate (1,3-pddadp) was prepared, chromatographically isolated as its isomer trans(O₅O₆)-Cs[Fe(1,3-pddadp)] · 2H₂O, and characterized. The trans(O₅O₆) configuration of the iron(III) compound was found to dominate and this geometry was established by means of IR spectroscopy and Density Functional Theory (DFT). Structural data correlating the octahedral geometry of the [Fe(1,3-pddadp)]⁻ unit and an extensive strain analysis are discussed in relation to the information obtained for similar complexes. Antibacterial activities of the free ligand and its corresponding iron(III) complex towards common Gram-negative and Gram-positive bacteria are reported as well.     

Square-planar copper(II) complexes with a novel tetradentate amido-carboxylate ligand. Crystal structure of [Co(H2O)6][Cu(mda)] · 2H2O

A novel O—N—N—O-type tetradentate ligand H₄mda (H₄mda = malamido-N,N-diacetic acid) and the corresponding square-planar copper(II) complexes have been prepared and characterized. The mda^4– ligand coordinates to the copper(II) ion via two pairs of deprotonated ligating atoms (two carboxylate oxygens and two deprotonated amide nitrogens) with in-plane square chelation. A four-coordinate, square-planar geometry has been established crystallographically for the [Co(H₂O)₆][Cu(mda)] · 2H₂O complex. Structural data correlating the square-planar geometry of the [Cu(mda)]^2– unit are discussed in relation to information obtained for similar complexes. The i.r., electronic, absorption and reflectance spectra of the complexes are analysed in comparison with related complexes of known geometries.     

Design of a fraction collector for capillary array electrophoresis

This paper describes a prototype instrument for high-throughput fraction collection with capillary array electrophoresis (CAE). The design of the system was based on a comprehensive collection approach, in which fractions from all capillaries were simultaneously collected in individual collection microwells in predefined time intervals. The location of the fractions in the microwells on the collection plate was determined by monitoring the individual zone velocities close to the end of each capillary. The collection microwell plate was fabricated from buffer-saturated agarose gel, which maintained permanent electrical contact with the separation capillaries during the collection process. Since the collection gel plate consisted of over 90% water, liquid evaporation from the collection wells was minimized. A 12-capillary array instrument was built with two-point detection using a side illumination scheme. The collection performance was demonstrated by reinjection of selected fractions of a double-stranded DNA (dsDNA) separation. The identity of collected DNA fragments was confirmed by PCR and sequencing.     

Semiempirical and ab initio transition state calculations for the transformation of N-acetyltetrazoles into corresponding 1,3,4-oxadiazoles

The transformation of 2-acetyl-5-substituted-tetrazoles into the corresponding 1,3,4-oxadiazoles was studied with the semiempirical and ab initio methods. Two mechanisms, one with two transition states and the other with three, were elucidated by . The first mechanism supported by PM3 and MNDO has a two-step, almost concerted, mechanism for the elimination of a nitrogen molecule from the tetrazole ring and formation of the oxadiazole product from an open-chain intermediate through carbon C₅ and acetyl oxygen bond formation. The second mechanism supported by AM1 and MINDO/3 breaks the elimination of the nitrogen molecule into two steps: first breaking the N₄-C₅ and then the N₂-N₃ bonds. Even when the AM1 and MINDO/3 transition state structures were optimized by PM3 and MNDO, the obtained transition states present only one bond breaking. The HF/STO-3G and HF/3-21G ab initio methods agree with the first mechanism where two bonds are breaking almost simultaneously. Despite the disagreement in the mechanism of the nitrogen elimination, the transition state that presents the product formation from open-chain intermediates is quite similar for all methods studied. The semiempirical calculation of this transition state is possible only if it is assumed that it has biradical character. The activation energies calculated by PM3 seem to be insensitive to the nature of the substituents.     

Hexafluoro­iodium(VII) hexa­fluoro­arsenate

The structure of hexa­fluoro­iodium(VII) hexa­fluoro­arsenate, IF₆AsF₆, has been determined by X‐ray diffraction using a single crystal grown from a saturated solution in anhydrous HF. IF₆AsF₆ crystallizes in the cubic space group Pa with a simple NaCl‐like ionic packing. The I and As atoms occupy the 4a and 4b Wyckoff positions, respectively, with symmetry.     

Coherence for closed categories with biproducts

A coherence result for symmetric monoidal closed categories with biproducts is shown in this paper. It is also explained how to prove coherence for compact closed categories with biproducts and for dagger compact closed categories with dagger biproducts by using the same technique.