The Supercore for Normal Form Games

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.

Depletion of the heaviest stable N isotope is associated with NH4 +/NH3 toxicity in NH4 +-fed plants

Background: In plants, nitrate (NO(3)(-)) nutrition gives rise to a natural N isotopic signature (delta(15)N), which correlates with the delta(15)N of the N source. However, little is known about the relationship between the delta(15)N of the N source and the (14)N/(15)N fractionation in plants under ammonium (NH(4)(+)) nutrition. When NH(4)(+) is the major N source, the two forms, NH(4)(+) and NH(3), are present in the nutrient solution. There is a 1.025 thermodynamic isotope effect between NH(3) (g) and NH(4)(+)(aq) which drives to a different delta(15)N. Nine plant species with different NH(4)(+)-sensitivities were cultured hydroponically with NO(3)(-) or NH(4)(+) as the sole N sources, and plant growth and delta(15)N were determined. Short-term NH(4)(+)/NH(3) uptake experiments at pH 6.0 and 9.0 (which favours NH(3) form) were carried out in order to support and substantiate our hypothesis. N source fractionation throughout the whole plant was interpreted on the basis of the relative transport of NH(4)(+) and NH(3). -- Results: Several NO(3)(-)-fed plants were consistently enriched in (15)N, whereas plants under NH(4)(+) nutrition were depleted of (15)N. It was shown that more sensitive plants to NH(4)(+) toxicity were the most depleted in (15)N. In parallel, N-deficient pea and spinach plants fed with (15)NH(4)(+) showed an increased level of NH(3) uptake at alkaline pH that was related to the (15)N depletion of the plant. Tolerant to NH(4)(+) pea plants or sensitive spinach plants showed similar trend on (15)N depletion while slight differences in the time kinetics were observed during the initial stages. The use of RbNO(3) as control discarded that the differences observed arise from pH detrimental effects. -- Conclusions: This article proposes that the negative values of delta(15)N in NH(4)(+)-fed plants are originated from NH(3) uptake by plants. Moreover, this depletion of the heavier N isotope is proportional to the NH(4)(+)/NH(3) toxicity in plants species. Therefore, we hypothesise that the low affinity transport system for NH(4)(+) may have two components: one that transports N in the molecular form and is associated with fractionation and another that transports N in the ionic form and is not associated with fractionation.

Stereoselective inverse conjugate addition of nitrogen and carbon nucleophiles to allenyl phosphine oxide. Synthesis of α,β-unsaturated phosphine oxides

Issue in Honor of Prof. Paweł Kafarski

A novel form of human disease with a protease-sensitive prion protein and heterozygosity methionine/valine at codon 129: Case report

Background: Sporadic Creutzfeldt-Jakob disease (sCJD) is a rare neurodegenerative disorder in humans included in the group of Transmissible Spongiform Encephalopathies or prion diseases. The vast majority of sCJD cases are molecularly classified according to the abnormal prion protein (PrPSc) conformations along with polymorphism of codon 129 of the PRNP gene. Recently, a novel human disease, termed "protease-sensitive prionopathy", has been described. This disease shows a distinct clinical and neuropathological phenotype and it is associated to an abnormal prion protein more sensitive to protease digestion. Case presentation: We report the case of a 75-year-old-man who developed a clinical course and presented pathologic lesions compatible with sporadic Creutzfeldt-Jakob disease, and biochemical findings reminiscent of "protease-sensitive prionopathy". Neuropathological examinations revealed spongiform change mainly affecting the cerebral cortex, putamen/globus pallidus and thalamus, accompanied by mild astrocytosis and microgliosis, with slight involvement of the cerebellum. Confluent vacuoles were absent. Diffuse synaptic PrP deposits in these regions were largely removed following proteinase treatment. PrP deposition, as revealed with 3F4 and 1E4 antibodies, was markedly sensitive to pre-treatment with proteinase K. Molecular analysis of PrPSc showed an abnormal prion protein more sensitive to proteinase K digestion, with a five-band pattern of 28, 24, 21, 19, and 16 kDa, and three aglycosylated isoforms of 19, 16 and 6 kDa. This PrPSc was estimated to be 80% susceptible to digestion while the pathogenic prion protein associated with classical forms of sporadic Creutzfeldt-Jakob disease were only 2% (type VV2) and 23% (type MM1) susceptible. No mutations in the PRNP gene were found and genotype for codon 129 was heterozygous methionine/valine. Conclusions: A novel form of human disease with abnormal prion protein sensitive to protease and MV at codon 129 was described. Although clinical signs were compatible with sporadic Creutzfeldt-Jakob disease, the molecular subtype with the abnormal prion protein isoforms showing enhanced protease sensitivity was reminiscent of the "protease-sensitive prionopathy". It remains to be established whether the differences found between the latter and this case are due to the polymorphism at codon 129. Different degrees of proteinase K susceptibility were easily determined with the chemical polymer detection system which could help to detect proteinase-susceptible pathologic prion protein in diseases other than the classical ones.

Synthesis and stereochemical assignments of diastereomeric Ni(II) complexes of glycine Schiff base with (R)-2-(N-{2-[N-alkyl-N-(1-phenylethyl)-amino]acetyl}amino) benzophenone; a case of configurationally stable stereogenic nitrogen

A family of chiral ligands derived from alpha-phenylethylamine and 2-aminobenzophenone were prepared by alkylation of the nitrogen atom. Upon reaction with glycine and a Ni(II) salt, these ligands were transformed into diastereomeric complexes, as a result of the configurational stability of the stereogenic nitrogen atom. Different diastereomeric ratios were observed depending on the substituent R introduced in the starting ligand, and stereochemical assignments were based on X-ray analysis, along with NMR studies and optical rotation measurements.

Beyond Q-Resolution and Prenex Form: a Proof System for Quantified Constraint Satisfaction

We consider the quanti fied constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quanti fication, whether or not the sentence is true on the structure. We present a proof system for certifying the falsity of QCSP instances and develop its basic theory; for instance, we provide an algorithmic interpretation of its behavior. Our proof system places the established Q-resolution proof system in a broader context, and also allows us to derive QCSP tractability results.

PGPRs and nitrogen-fixing legumes: a perfect team for efficient Cd phytoremediation?

Cadmium (Cd) is a toxic, biologically non-essential and highly mobile metal that has become an increasingly important environmental hazard to both wildlife and humans. In contrast to conventional remediation technologies, phytoremediation based on legume rhizobia symbiosis has emerged as an inexpensive decontamination alternative which also revitalize contaminated soils due to the role of legumes in nitrogen cycling. In recent years, there is a growing interest in understanding symbiotic legume rhizobia relationship and its interactions with Cd. The aim of the present review is to provide a comprehensive picture of the main effects of Cd in N-2-fixing leguminous plants and the benefits of exploiting this symbiosis together with plant growth promoting rhizobacteria to boost an efficient reclamation of Cd-contaminated soils.