Davenport constant for finite abelian groups

For a finite abelian group G, we investigate the length of a sequence of elements of G that is guaranteed to have a subsequence with product identity of G. In particular, we obtain a bound on the length which takes into account the repetitions of elements of the sequence, the rank and the invariant factors of G. Consequently, we see that there are plenty of such sequences whose length could be much shorter than the best known upper bound for the Davenport constant of G, which is the least integer s such that any sequence of length s in G necessarily contains a subsequence with product identity. We also show that the Davenport constant for the multiplicative group of reduced residue classes modulo n is comparatively large with respect to the order of the group, which is φ(n),when n is in certain thin subsets of positive integers. This is done by studying the Carmichael’s lambda function, defined as the maximal multiplicative order of any reduced residue modulo n, along these subsets.     

Lehmer -tuples

Generalizing a classical problem of Lehmer, in this paper we provide an asymptotic result for the number of Lehmer -tuples.

     

Projective modules and prime submodules

In this paper, we use Zorn’s Lemma, multiplicatively closed subsets and saturated closed subsets for the following two topics (i) The existence of prime submodules in some cases (ii) The proof that submodules with a certain property satisfy the radical formula. We also give a partial characterization of a submodule of a projective module which satisfies the prime property.     

Values of Dirichlet <Emphasis Type=Italic>L</Emphasis>-functions,Gauss sums and trigonometric sums

Motivated by the classical work of Ramanujan and recent work of Berndt and Zaharescu, we establish certain infinite families of identities relating values of Dirichlet L-functions at positive integers to Gauss sums and trigonometric sums twisted with characters.     

On linear combinations of special values of L-functions

Using a specific evaluation method for L-functions, it is shown that character values and weighted averages of Gauss sums can be well approximated by linear combinations of the algebraic parts of special values of L-functions under correct parity conditions. This is a surprising universal property of these special values since the coefficients of the resulting combinations turn out to be independent of the character but its parity.     

Molecularly imprinted cryogel as a pH-responsive delivery system for doxorubicin

In this study, implantable and degradable molecularly imprinted cryogel was prepared for pH-responsive delivery of doxorubicin. Cryogel discs were synthesized using amino acid-based functional monomer with HEMA and gelatin. The molecularly imprinted discs were characterized by scanning electron microscopy, Fourier transform infrared spectroscopy, degradation and swelling tests. In vitro delivery experiments were carried out in order to examine the effects of medium pH and drug content. The degree of degradation of composite cryogels was found to be 83.45±1.86% after 56 days. The release profiles of DOX from molecularly imprinted cryogel discs exhibit a biphasic delivery. It was observed that an initial burst release step from 0 to 12 h was followed by a slower and sustained release. Release rate of DOX from cryogel discs increased in more acidic conditions. Kinetic studies showed that a combination of diffusion and erosion control is mainly responsible from the general release behaviors of molecularly imprinted cryogel discs.     

Series representations in the spirit of Ramanujan

Using an integral transform with a mild singularity, we obtain series representations valid for specific regions in the complex plane involving trigonometric functions and the central binomial coefficient which are analogues of the types of series representations first studied by Ramanujan over certain intervals on the real line. We then study an exponential type series rapidly converging to the special values of L-functions and the Riemann zeta function. In this way, a new series converging to Catalan?s constant with geometric rate of convergence less than a quarter is deduced. Further evaluations of some series involving hyperbolic functions are also given.     

Discrepancy of Fractions with Divisibility Constraints

We provide bounds for the absolute discrepancy of sequences of fractions with denominators streaming in a given arithmetic progression and satisfying divisibility constraints.     

Radioactive ore analysis by optimized radioisotope X-ray fluorescence technique

A method for analyzing U and Th in radioactive ores by radioisotope excited X-ray fluorescence is described. For the proposed analysis, the theoretical and experimental factors that affect the sensitivity of the radioisotope XRF technique were investigated. Minimum detection limits of 13 ppm and 108 ppm can be achieved for U and Th, respectively, with a total counting time of 1000 s on a powdered ore sample. Results obtained in the analyses of radioactive ores from Turkey and BL-5 candidate reference uranium ores from CANMET (Canada Centre for Mineral and Energy Technology) are reported.