Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar delta function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called delta' interaction. We emphasize that there is little resemblance between the delta' interaction and what its name suggests.

Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta-function source. Using the techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.

3C 273 variability at 7 mm: evidence of shocks and precession in the jet

We report on four years of observations of 3C 273 at 7mm obtained with the Itapetinga radio telescope, in Brazil, between 2009 and 2013. We detected a flare in 2010 March, when the flux density increased by 50 per cent and reached 35 Jy. After the flare, the flux density started to decrease and reached values lower than 10 Jy. We suggest that the 7-mm flare is the radio counterpart of the γ -ray flare observed by the Fermi Large Area Telescope in 2009 September, in which the flux density at high energies reached a factor of 50 of its average value. A delay of 170 d between the radio and γ -ray flares was revealed using the discrete correlation function (DCF) that can be interpreted in the context of a shock model, in which each flare corresponds to the formation of a compact superluminal component that expands and becomes optically thin at radio frequencies at latter epochs. The differences in flare intensity between frequencies and at different times are explained as a consequence of an increase in the Doppler factor δ, as predicted by the 16-yr precession model proposed by Abraham & Romero. This increase has a large effect on boosting at high frequencies while it does not affect the observed optically thick radio emission too much. We discuss other observable effects of the variation in δ, such as the increase in the formation rate of superluminal components, the variations in the time delay between flares and the periodic behaviour of the radio light curve that we have found to be compatible with changes in the Doppler factor.

Reduced fertility in mice deficient for the POU protein sperm-1

Members of the POU-homeodomain gene family encode transcriptional regulatory molecules that play important roles in terminal differentiation of many organ systems. Sperm-1 (Sprm-1) is a POU domain factor that is exclusively expressed in the differentiating male germ cell. We show here that the Sprm-1 protein is expressed in the haploid spermatid and that 129/Sv Sprm-1(−/−) mice are subfertile when compared with wild-type or heterozygous littermates yet exhibit normal testicular morphology and produce normal numbers of mobile spermatozoa. Our data suggest that the Sprm-1 protein plays a discrete regulatory function in the haploid spermatid, which is required for the optimal function, but not the terminal differentiation, of the male germ cell.

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

One-dimensional interacting anyon gas: Low-energy properties and haldane exclusion statistics

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.

Opposite Effects of Delta-9-Tetrahydrocannabinol and Cannabidiol on Human Brain Function and Psychopathology

Delta-9-tetrahydrocannabinol (Delta-9-THC) and Cannabidiol (CBD), the two main ingredients of the Cannabis sativa plant have distinct symptomatic and behavioral effects. We used functional magnetic resonance imaging (fMRI) in healthy volunteers to examine whether Delta-9-THC and CBD had opposite effects on regional brain function. We then assessed whether pretreatment with CBD can prevent the acute psychotic symptoms induced by Delta-9-THC. Fifteen healthy men with minimal earlier exposure to cannabis were scanned while performing a verbal memory task, a response inhibition task, a sensory processing task, and when viewing fearful faces. Subjects were scanned on three occasions, each preceded by oral administration of Delta-9-THC, CBD, or placebo. BOLD responses were measured using fMRI. In a second experiment, six healthy volunteers were administered Delta-9-THC intravenously on two occasions, after placebo or CBD pretreatment to examine whether CBD could block the psychotic symptoms induced by Delta-9-THC. Delta-9-THC and CBD had opposite effects on activation relative to placebo in the striatum during verbal recall, in the hippocampus during the response inhibition task, in the amygdala when subjects viewed fearful faces, in the superior temporal cortex when subjects listened to speech, and in the occipital cortex during visual processing. In the second experiment, pretreatment with CBD prevented the acute induction of psychotic symptoms by Delta-9-tetrahydrocannabinol. Delta-9-THC and CBD can have opposite effects on regional brain function, which may underlie their different symptomatic and behavioral effects, and CBD`s ability to block the psychotogenic effects of Delta-9-THC. Neuropsychopharmacology (2010) 35, 764-774; doi:10.1038/npp.2009.184; published online 18 November 2009

Modulation of Mediotemporal and Ventrostriatal Function in Humans by Delta 9-Tetrahydrocannabinol A Neural Basis for the Effects of Cannabis sativa on Learning and Psychosis

Context: Cannabis sativa use can impair verbal learning, provoke acute psychosis, and increase the risk of schizophrenia. It is unclear where C sativa acts in the human brain to modulate verbal learning and to induce psychotic symptoms. Objectives: To investigate the effects of 2 main psychoactive constituents of C sativa, Delta 9-tetrahydrocannabinol (Delta 9-THC) and cannabidiol, on regional brain function during verbal paired associate learning. Design: Subjects were studied on 3 separate occasions using a block design functional magnetic resonance imaging paradigm while performing a verbal paired associate learning task. Each imaging session was preceded by the ingestion of Delta 9-THC (10 mg), cannabidiol (600 mg), or placebo in a double-blind, randomized, placebo-controlled, repeated-measures, within-subject design. Setting: University research center. Participants: Fifteen healthy, native English-speaking, right-handed men of white race/ethnicity who had used C sativa 15 times or less and had minimal exposure to other illicit drugs in their lifetime. Main Outcome Measures: Regional brain activation ( blood oxygen level-dependent response), performance in a verbal learning task, and objective and subjective ratings of psychotic symptoms, anxiety, intoxication, and sedation. Results: Delta 9-Tetrahydrocannabinol increased psychotic symptoms and levels of anxiety, intoxication, and sedation, whereas no significant effect was noted on these parameters following administration of cannabidiol. Performance in the verbal learning task was not significantly modulated by either drug. Administration of Delta 9-THC augmented activation in the parahippocampal gyrus during blocks 2 and 3 such that the normal linear decrement in activation across repeated encoding blocks was no longer evident. Delta 9-Tetrahydrocannabinol also attenuated the normal time-dependent change in ventrostriatal activation during retrieval of word pairs, which was directly correlated with concurrently induced psychotic symptoms. In contrast, administration of cannabidiol had no such effect. Conclusion: The modulation of mediotemporal and ventrostriatal function by Delta 9-THC may underlie the effects of C sativa on verbal learning and psychotic symptoms, respectively.

Dynamic delta hedging of autocallables under a discrete rebalancing context

This work tests different delta hedging strategies for two products issued by Banco de Investimento Global in 2012. The work studies the behaviour of the delta and gamma of autocallables and their impact on the results when delta hedging with different rebalancing periods. Given its discontinuous payoff and path dependency, it is suggested the hedging portfolio is rebalanced on a daily basis to better follow market changes. Moreover, a mixed strategy is analysed where time to maturity is used as a criterion to change the rebalancing frequency.

PPAR beta/delta Agonists Modulate Platelet Function via a Mechanism Involving PPAR Receptors and Specific Association/Repression of PKC alpha-Brief Report

Objectives-Peroxisome proliferator-activated receptor beta/delta (PPAR beta/delta) is a nuclear receptor found in platelets. PPAR beta/delta agonists acutely inhibit platelet function within a few minutes of addition. As platelets are anucleated, the effects of PPAR beta/delta agonists on platelets must be nongenomic. Currently, the particular role of PPAR beta/delta receptors and their intracellular signaling pathways in platelets are not known. Methods and Results-We have used mice lacking PPAR beta/delta (PPAR beta/delta(-/-)) to show the effects of the PPAR beta/delta agonist GW501516 on platelet adhesion and cAMP levels are mediated specifically by PPAR beta/delta, however GW501516 had no PPAR beta/delta-specific effect on platelet aggregation. Studies in human platelets showed that PKC alpha, which can mediate platelet activation, was bound and repressed by PPAR beta/delta after platelets were treated with GW501516. Conclusions-These data provide evidence of a novel mechanism by which PPAR receptors influence platelet activity and thereby thrombotic risk. (Arterioscler Thromb Vasc Biol. 2009; 29: 1871-1873.)

Some problems of discrete function theory

An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.