A note on the computation of the Frobenius number of a numerical semigroup

In this note we observe that the Frobenius number and therefore the conductor of a numerical semigroup can be obtained from the maximal socle degree of the quotient of the corresponding semigroup algebra by the ideal generated by the biggest generator of the semigroup.Comment: Some typos in the introduction have been correcte

Numerical semigroups with large embedding dimension satisfy Wilf's conjecture

We give an affirmative answer to Wilf's conjecture for numerical semigroups satisfying 2 \nu \geq m, where \nu and m are respectively the embedding dimension and the multiplicity of a semigroup. The conjecture is also proved when m \leq 8 and when the semigroup is generated by a generalized arithmetic sequence.Comment: 13 page

Quantum-Aware Software Defined Networks

Software Defined Networks (SDN) represent a major paradigm change in communications networks. It provides a level of abstraction and independence from the traditional networking practice that allows for a fast path of innovation and, specifically, opens new opportunities for Quantum Key Distribution (QKD) networks. In this contribution we explore the implications of this paradigm for the deployment of QKD in practice from the point of view of telecommunications? providers, network equipment manufacturers and applied research and development. We propose a generic quantum-aware SDN architecture and two applications, a generic end to end encryption one and other for the network infrastructure itself

Las fallas del recinto de la Alhambra : Faults in the Alhambra area

The Alhambra is built on a conglomeratic formation, known as the Alhambra Formation, whose age is Pliocene to Lower Pleistocene and has a visible thickness of 200 metres. The western part of the San Pedro escarpment corresponds to a fault-scarp with some retreat; the fault-plane outcrops in the innermost part of the escarpment, showing normal displacement and NW-SE strike with NE steep dip. This fault is the most important one of a set that outcrops along the northern hillslope of the Alhambra. Several topographic steps with NW-SE orientation are interpreted as retreated fault-scarps. In some cases, the activity of these faults seems to be very recent and maybe related to earthquakes. The seismic risk associated with these faults (and maybe some not-outcropping ones) can be taken to be moderate, as some historical damages have been reported concerning the Alhambra walls and the fence. In this respect, the Alhambra fence has numerous cracks geometrically related to fault planes outcropping in the Alhambra Formation, i.e. faults and cracks are continuous and have similar strike and dip. We hypothesize that these cracks are due to small displacements along the faults, occurred during recent earthquakes in the region. These faults constitute mechanical discontinuities, which represent a supplementary risk, because they contribute to reduce the stability of the entire rock massif

Ordering in the dilute weakly-anisotropic antiferromagnet Mn(0.35)Zn(0.65)F2

The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated by neutron scattering in zero field. The Bragg peaks observed below the Neel temperature TN (approximately 10.9 K) indicate stable antiferromagnetic long-range ordering at low temperature. The critical behavior is governed by random-exchange Ising model critical exponents (nu approximately 0.69 and gamma approximately 1.31), as reported for Mn(x)Zn(1-x)F2 with higher x and for the isostructural compound Fe(x)Zn(1-x)F2. However, in addition to the Bragg peaks, unusual scattering behavior appears for |q|>0 below a glassy temperature Tg approximately 7.0 K. The glassy region T<Tg corresponds to that of noticeable frequency dependence in earlier zero-field ac susceptibility measurements on this sample. These results indicate that long-range order coexists with short-range nonequilibrium clusters in this highly diluted magnet.Comment: 7 pages, 5 figure

Solutions of Gross-Pitaevskii equations beyond the hydrodynamic approximation: Application to the vortex problem

We develop the multiscale technique to describe excitations of a Bose-Einstein condensate (BEC) whose characteristic scales are comparable with the healing length, thus going beyond the conventional hydrodynamical approximation. As an application of the theory we derive approximate explicit vortex and other solutions. The dynamical stability of the vortex is discussed on the basis of the mathematical framework developed here, the result being that its stability is granted at least up to times of the order of seconds, which is the condensate lifetime. Our analytical results are confirmed by the numerical simulations.Comment: To appear in Phys. Rev.

Sensitization of cervix cancer cells to Adriamycin by Pentoxifylline induces an increase in apoptosis and decrease senescence

<p>Abstract</p> <p>Background</p> <p>Chemotherapeutic drugs like Adriamycin (ADR) induces apoptosis or senescence in cancer cells but these cells often develop resistance and generate responses of short duration or complete failure. The methylxantine drug Pentoxifylline (PTX) used routinely in the clinics setting for circulatory diseases has been recently described to have antitumor properties. We evaluated whether pretreatment with PTX modifies apoptosis and senescence induced by ADR in cervix cancer cells.</p> <p>Methods</p> <p>HeLa (HPV 18+), SiHa (HPV 16+) cervix cancer cells and non-tumorigenic immortalized HaCaT cells (control) were treated with PTX, ADR or PTX + ADR. The cellular toxicity of PTX and survival fraction were determinated by WST-1 and clonogenic assay respectively. Apoptosis, caspase activation and ADR efflux rate were measured by flow cytometry, senescence by microscopy. IκBα and DNA fragmentation were determinated by ELISA. Proapoptotic, antiapoptotic and senescence genes, as well as HPV-E6/E7 mRNA expression, were detected by time real RT-PCR. p53 protein levels were assayed by Western blot.</p> <p>Results</p> <p>PTX is toxic (WST-1), affects survival (clonogenic assay) and induces apoptosis in cervix cancer cells. Additionally, the combination of this drug with ADR diminished the survival fraction and significantly increased apoptosis of HeLa and SiHa cervix cancer cells. Treatments were less effective in HaCaT cells. We found caspase participation in the induction of apoptosis by PTX, ADR or its combination. Surprisingly, in spite of the antitumor activity displayed by PTX, our results indicate that methylxantine, <it>per se </it>does not induce senescence; however it inhibits senescence induced by ADR and at the same time increases apoptosis. PTX elevates IκBα levels. Such sensitization is achieved through the up-regulation of proapoptotic factors such as <it>caspase </it>and <it>bcl </it>family gene expression. PTX and PTX + ADR also decrease E6 and E7 expression in SiHa cells, but not in HeLa cells. p53 was detected only in SiHa cells treated with ADR.</p> <p>Conclusion</p> <p>PTX is a good inducer of apoptosis but does not induce senescence. Furthermore, PTX reduced the ADR-induced senescence and increased apoptosis in cervix cancer cells.</p

Aportaciones a la flora de Galicia, IX

En este trabajo se mencionan 53 plantas de diverso interés para la flora de Galicia o zonas próximas. Se incluyen 3 novedades para España (Sesamoides minor (Lange) O. Kuntze x S. purpurascens (L.) G. López, Hedychium gardnerianum Sheppard ex Ker-Gawler y Oxalis incarnata L.) y otra para Portugal (Bromus hordeaceus L. subsp. ferronii (Mabille) P.M. Smith), 3 novedades regionales (Oxalis incarnata L., Antirrhinum latifolium Mill., Sisyrinchium striatum Mill.), 16 novedades provinciales (Ranunculus bulbosus L. subsp. aleae (Willk.) Rouy & Fouc. var. adscendens (Brot.) Pinto da Silva, Ranunculus peltatus subsp. peltatus var. microcarpus Meikle, Dianthus laricifolius subsp. merinoi (M. Laínz) M. Laínz, Spartium junceum L., Sanicula europea L., Tordylium maximum L., Euphorbia flavicoma DC. subsp. occidentalis M. Laínz, Campanula medium L., Centaurea melitensis L., Festuca durandoi Clauson in Billot subsp. capillifolia (Pau ex Willk.) Rivas Ponce, Cebolla & M.B. Crespo var. livida (Hack.) Rivas-Ponce, Cebolla & M.B. Crespo, Phalaris minor Retz, Carex distans L., Carex umbrosa Hornem. subsp. umbrosa) y otras 40 de interés diverso, bien ecológico, corológico o taxonómico. También, y a la luz de más información, eliminamos del catálogo de la flora vascular de Galicia Iberis contracta subsp. welwitschii (Boiss.) Moreno y Arctium lappa L. Se lectotipifica Euphorbia polygalifolia subsp. hirta (Lange) M. Laínz y Senecio doria var. subintegrum Merino

Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients

Motivated by the study of matter waves in Bose-Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrodinger equations with inhomogeneous parameters, including a linear coupling. For that system we prove the existence of two different kinds of homoclinic solutions to the origin describing solitary waves of physical relevance. We use a Krasnoselskii fixed point theorem together with a suitable compactness criterion.Comment: 16 page

Patients with primary immunodeficiencies are a reservoir of poliovirus and a risk to polio eradication

ABSTARCT: Immunodeficiency-associated vaccine-derived polioviruses (iVDPVs) have been isolated from primary immunodeficiency (PID) patients exposed to oral poliovirus vaccine (OPV). Patients may excrete poliovirus strains for months or years; the excreted viruses are frequently highly divergent from the parental OPV and have been shown to be as neurovirulent as wild virus. Thus, these patients represent a potential reservoir for transmission of neurovirulent polioviruses in the post-eradication era. In support of WHO recommendations to better estimate the prevalence of poliovirus excreters among PIDs and characterize genetic evolution of these strains, 635 patients including 570 with primary antibody deficiencies and 65 combined immunodeficiencies were studied from 13 OPV-using countries. Two stool samples were collected over 4 days, tested for enterovirus, and the poliovirus positive samples were sequenced. Thirteen patients (2%) excreted polioviruses, most for less than 2 months following identification of infection. Five (0.8%) were classified as iVDPVs (only in combined immunodeficiencies and mostly poliovirus serotype 2). Non-polio enteroviruses were detected in 30 patients (4.7%). Patients with combined immunodeficiencies had increased risk of delayed poliovirus clearance compared to primary antibody deficiencies. Usually, iVDPV was detected in subjects with combined immunodeficiencies in a short period of time after OPV exposure, most for less than 6 months. Surveillance for poliovirus excretion among PID patients should be reinforced until polio eradication is certified and the use of OPV is stopped. Survival rates among PID patients are improving in lower and middle income countries, and iVDPV excreters are identified more frequently. Antivirals or enhanced immunotherapies presently in development represent the only potential means to manage the treatment of prolonged excreters and the risk they present to the polio endgame. Keywords: Poliovirus eradication, Immunodeficiency-associated vaccine-derived polioviruses, Oral poliovirus vaccine, Humoral immunodeficiency, Combined immunodeficiency, Primary immunodeficienc