Using an integral representation of the logarithmic derivative of the corresponding Selberg zeta function, we prove Stieltjes-type expressions for higher Euler constants on non-compact hyperbolic Riemann surfaces of finite volume with cusps. New upper and lower bounds are given for the constant term of this logarithmic derivative in a case of interest in Arakelov geometry.

The thesis examines the foreign direct investment (FDI) inflows in the Middle East and North Africa (MENA) region and, in order to achieve a better understanding of how MENA economies may attract ...

AIM To evaluate trends in DNA typing success rates of different skeletal elements from mass graves originating from conflicts that occurred in the former Yugoslavia (Bosnia and Herzegovina and Kosovo) during the 1990s, and to establish correlation between skeletal sample age and success of high throughput short tandem repeat (STR) typing in the large data set of the International Commission on Missing Persons. METHOD DNA extraction and short tandem repeat (STR) typing have been attempted on over 25000 skeletal samples. The skeletal samples originated from different geographical locations where the conflicts occurred and from different time periods from 1992 to 1999. DNA preservation in these samples was highly variable, but was often significantly degraded and of limited quantity. For the purpose of this study, processed samples were categorized according to skeletal sample type, sample age since death, and success rates tabulated. RESULTS Well-defined general trends in success rates of DNA analyses were observed with respect to the type of bone tested and sample age. The highest success rates were observed with samples from dense cortical bone of weight-bearing leg bones (femur 86.9%), whereas long bones of the arms showed significantly lower success (humerus 46.2%, radius 24.5%, ulna 22.8%). Intact teeth also exhibited high success rates (teeth 82.7%). DNA isolation from other skeletal elements differed considerably in success, making bone sample selection an important factor influencing success. CONCLUSION The success of DNA typing is related to the type of skeletal sample. By carefully evaluating skeletal material available for forensic DNA testing with regard to sample age and type of skeletal element available, it is possible to increase the success and efficiency of forensic DNA testing.

AIM To present a compendium of off-ladder alleles and other genotyping irregularities relating to rare/unexpected population genetic variation, observed in a large short tandem repeat (STR) database from Bosnia and Serbia. METHODS DNA was extracted from blood stain cards relating to reference samples from a population of 32800 individuals from Bosnia and Serbia, and typed using Promega's PowerPlex16 STR kit. RESULTS There were 31 distinct off-ladder alleles were observed in 10 of the 15 STR loci amplified from the PowerPlex16 STR kit. Of these 31, 3 have not been previously reported. Furthermore, 16 instances of triallelic patterns were observed in 9 of the 15 loci. Primer binding site mismatches that affected amplification were observed in two loci, D5S818 and D8S1179. CONCLUSION Instances of deviations from manufacturer's allelic ladders should be expected and caution taken to properly designate the correct alleles in large DNA databases. Particular care should be taken in kinship matching or paternity cases as incorrect designation of any of these deviations from allelic ladders could lead to false exclusions.

Building upon our work on explicit formulas for the Jorgenson-Lang fundamental class of functions, we deduce expressions for Euler constants in the case of Dedekind zeta function that are analoguous to the Stieltjes results for the Riemann zeta function.

Explicit formula for the fundamental class of functions ( Z, Z,Φ ) , introduced by J. Jorgenson and S. Lang, is given a new form valid for a more general fudge factor Φ. This is done for a larger class of test functions of generalized bounded variation.

Taking Weil’s point on adelic nature of explicit formulas, we extend the class of test functions to which his formula in Barner‐Burnol version holds.

A. Magyar's result on L p -bounds for a family of operators on k-spheres (k > 3) in Z" is improved to match the corresponding theorem for 2-spheres.

[1] Avdispahic, M., Smajlovic, L. An explicit formula and its application to the Selbergtrace formula, Monatsh. Math. 147 No. 3 (2006), 183-198.[2] Avdispahic, M., Smajlovic, L. Selberg trace formula as an explicit formula and theprime geodesic theorem (submitted)[3] Hejhal, D. A. The Selberg trace formula for PSL(2,R) Vol. II, Lecture Notes inMathematics 1001. Springer-Verlag, Berlin-Heidelberg 1983.[4] Iwaniec, H. Spectral methods of automorphic forms, Graduate Studies in Mathematics53. AMS, Providence 2002[5] Jorgenson, J., Kramer, J. On the error term of the prime geodesic theorem, ForumMath. 14 (2002), 901-913.

The purpose of this paper is to prove an analogue of A. Weil’s explicit formula for a fundamental class of functions, i.e. the class of meromorphic functions that have an Euler sum representation and satisfy certain a functional equation. The advance of this explicit formula is that it enlarges the class of allowed test functions, from the class of functions with bounded Jordan variation to the class of functions of -bounded variation. A condition posed to the test function at zero is also reconsidered.