Massive supersymmetric quantum gauge theory

We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one‐particle physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang‐Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.     

Moments of the maximum of normed partial sums of random variables with multidimensional indices

Summary For a set of i.i.d. random variables indexed by the positive integer d-dimensional lattice points we give conditions for the existence of moments of the supremum of normed partial sums, thereby obtaining results related to the Kolmogorov-Marcinkiewicz strong law of large numbers and the law of the iterated logarithm.     

On Asymptotic and Strict Monotonicity of a Sharper Lower Bound for Student’s t Percentiles

Let z _α and t _ν,α denote the upper 100α% points of a standard normal and a Student’s t _ν distributions respectively. It is well-known that for every fixed $0<\alpha <\frac{1}{2}$ and degree of freedom ν, one has t _ν,α ?>?z _α and that t _ν,α monotonically decreases to z _α as ν increases. Recently, Mukhopadhyay (Methodol Comput Appl Probab, 2009) found a new and explicit expression b _ν (?>?1) such that t _ν,α ?>?b _ν z _α for every fixed $0<\alpha <\frac{1}{2}$ and ν. He also showed that b _ν converges to 1 as ν increases. In this short note, we prove three key results: (i) $\log(b_{\nu+1}/b_{\nu})\sim -\frac{1}{4}\nu^{-2}$ for large enough ν, (ii) b _ν strictly decreases as ν increases, and (iii) $b_{\nu}\sim 1+\frac14\nu^{-1}+\frac1{32}\nu^{-2}$ for large enough ν.     

Synthesis of Morpholine-Based Analogues of (−)-Zampanolide and Their Biological Activity

We describe the convergent synthesis of three prototypical examples of a new class of analogues of the complex, cytotoxic marine macrolide (−)-zampanolide that incorporate an embedded N-substituted morpholine moiety in place of the natural tetrahydropyran ring. The final construction of the macrolactone core was based on a high-yielding intramolecular HWE olefination, while the hemiaminal-linked side chain was elaborated through a stereoselective, BINAL-H-mediated addition of (Z,E)-sorbamide to a macrocyclic aldehyde precursor. The synthesis of the common functionalized morpholine building block involved two consecutive epoxide openings with tosylamide and the product of the first opening reaction, respectively, as nucleophiles. Of the three morpholino-zampanolides investigated, the N-acetyl and the N-benzoyl derivatives both exhibited nanomolar antiproliferative activity, thus being essentially equipotent with the natural product. In contrast, the activity of the N-tosyl derivative was significantly reduced.     

A Maxtrimmed St. Petersburg Game

Let \(S_n\), \(n\ge 1\), describe the successive sums of the payoffs in the classical St. Petersburg game. The celebrated Feller weak law states that \(\frac{S_n}{n\log _2 n}\mathop {\rightarrow }\limits ^{p}1\) as \(n\rightarrow \infty \). It is also known that almost sure convergence fails. However, Csörg? and Simons (Stat Probab Lett 26:65–73, 1996) have shown that almost sure convergence holds for trimmed sums, that is, for \(S_n-\max _{1\le k\le n}X_k\). Since our actual distribution is discrete there may be ties. Our main focus in this paper is on the “maxtrimmed sum”, that is, the sum trimmed by the random number of observations that are equal to the largest one. We prove an analog of Martin-Löf’s (J Appl Probab 22:634–643, 1985) distributional limit theorem for maxtrimmed sums, but also for the simply trimmed ones, as well as for the “total maximum”. In a final section, we interpret these findings in terms of sums of (truncated) Poisson random variables.     

Methoxokomplexe drei-, vier- und fünfwertiger Zentralatome

The complex formation with CH₃O^? of As^III, Sb^III, Ge^IV, Nb^IV, Se^IV, Te^IV, Ti^IV, Sn^IV and Mo^V has been investigated in absolute methanolic solutions containing (CH₃)₄NCl, LiCl, or Lithiumtosylate (μ = 1; 20.0°) by means of pH-titrations. The relations between the stoichiometry of the reactions and the shape of the buffer regions, as well as the concentration-dependance of these buffer regions are discussed.     

Extension of the GOOD assay for genotyping single nucleotide polymorphisms by matrix-assisted laser desorption/ionization mass spectrometry

Over the past years several methods using mass spectrometry for high-throughput genotyping of single nucleotide polymorphisms (SNPs) have been developed. Most of these procedures require stringent purification. Only the GOOD assay does not need any sample purification. Here, several new implementations of this assay are presented. The molecular biological procedure of the GOOD assays is based on the principle that the analysis of DNA by matrix-assisted laser desorption/ionization (MALDI) is strongly dependent on the charge state. A 100-fold increase in sensitivity can be achieved if the analyzed DNA product is conditioned by a chemical procedure termed 'charge-tagging'. The GOOD assay starts with a PCR; allele-specific DNA molecules are generated by extension of modified primers. These contain up to three phosphorothioates and optionally a quaternary ammonium charged group with ddNTPs or alpha-S-ddNTPs. Then the unmodified part of the primers is digested by phosphodiesterase II and the negative charges of the phosphorothioates are neutralized by an alkylation reaction resulting in charge-tagged DNA products. Through the use of a novel DNA polymerase for the primer extension, which preferably incorporates ddNTPs over dNTPs, an enzymatic degradation of residual dNTPs from the PCR is not required. Additionally, the unique property of charge-tag technology is demonstrated to detect specifically on the same sample allele-specific DNA products carrying a positive charge-tag in the positive ion mode while products carrying a negative charge-tag are analyzed in the negative ion mode. We also generated zwitterionic allele-specific products that were detectable with high sensitivity in positive ion mode. The findings of this study raise interesting questions about the ionization process of nucleic acids in MALDI. The new variations of the GOOD assay were applied to genotype SNPs of a candidate gene for cardiovascular disease.