Roots of the affine Cremona group

Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,...,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov.Comment: 4 page

Orientifold daughter of N=4 SYM and double-trace running

We study the orientifold daughter of N=4 super Yang-Mills as a candidate non-supersymmetric large N conformal field theory. In a theory with vanishing single-trace beta functions that contains scalars in the adjoint representation, conformal invariance might still be broken by renormalization of double-trace terms to leading order at large N. In this note we perform a diagrammatic analysis and argue that the orientifold daughter does not suffer from double-trace running. This implies an exact large N equivalence between this theory and a subsector of N=4 SYM.Comment: 12 page

Boundary and Interface CFTs from the Conformal Bootstrap

40 pages, many figures v2: new results on 3d O(N) bulk spectrum added, one appendix eliminated, typos corrected, references updated. v3: two references to high precision Monte Carlo data added; they nicely agree with our bootstrap calculations. Matches published version. v4: results for the extraordinary transition for N=2,3 removed: see added noteWe explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface transitions of the 3d Ising and other O(N) models through numerical solutions to the crossing equations with the method of determinants. In the extraordinary transition, where the low-lying spectrum of the surface operators is known, we use the bootstrap equations to obtain information on the bulk spectrum of the theory. In the ordinary transition the knowledge of the low-lying bulk spectrum allows to calculate the scale dimension of the relevant surface operator, which compares well with known results of two-loop calculations in 3d. Estimates of various OPE coefficients are also obtained. We also analyze in 4-epsilon dimensions the renormalization group interface between the O(N) model and the free theory and check numerically the results in 3d

Torus invariant divisors

Using the language of polyhedral divisors and divisorial fans we describe invariant divisors on normal varieties X which admit an effective codimension one torus action. In this picture X is given by a divisorial fan on a smooth projective curve Y. Cartier divisors on X can be described by piecewise affine functions h on the divisorial fan S whereas Weil divisors correspond to certain zero and one dimensional faces of it. Furthermore we provide descriptions of the divisor class group and the canonical divisor. Global sections of line bundles O(D_h) will be determined by a subset of a weight polytope associated to h, and global sections of specific line bundles on the underlying curve Y.Comment: 16 pages; 5 pictures; small changes in the layout, further typos remove

Nucleation and growth kinetics of CaCO3 crystals in the presence of foreign monovalent ions

The aim of this work is to study the effect of the presence of different monovalent ions (Na+, NH4+ and K+) on the nucleation and growth rates of CaCO3 precipitation. There is currently great interest in the precipitation of CaCO3 particles reusing CO2 rich flue gases and calcium-rich wastes, which implies the presence of foreign ions that can affect the crystallization process. Unseeded and seeded tests were carried out in a batch system to estimate the nucleation and growth kinetics, respectively. Tests with Na2CO3 and CaCl2 as precursors led to the classical calcite crystallization mechanism via vaterite formation at high supersaturations. On the other hand, the use of (NH4)2CO3 entailed lower pH and the presence of NH4+, which stabilized the vaterite and avoided its transformation into stable calcite crystals. Thus, faster nucleation kinetics by using Na2CO3 were obtained. To estimate the growth rate, tests with two initial seed loadings and types (micro and nano seed) were performed. The growth rate increased with the crystal size and decreased with the magma density. The results indicate that the ion effect on the growth rate seems to be related to the ionic radius of the foreign ion

Optimization of CaCO3 synthesis through the carbonation route in a packed bed reactor

This article presents an investigation on the recovery of CO2 from the combustion gases of the cement industry through a carbonation route in order to obtain Calcium Carbonate Nanoparticles (CCnP), which could find application as either polymer or cement fillers. Two different experimental setups, a Continuously Stirred Bubbling Reactor (CSBR) and a Packed Bed Reactor (PBR), were studied in order to improve the final product and enhance the process yield. The influence of the experimental parameters on the particle size and morphology was tested for both reactors. The process was intensified by employing the PBR, where cubic calcite particles smaller than 300 nm were synthesized and higher CO2 conversions were obtained with respect to the CSBR performance

Therapeutic Benefits of Body Percussion Using the BAPNE Method

Body percussion using to the BAPNE method is a means of cognitive stimulation with multiple applications. The aim of this research is to assess their full potential as a source of therapy. The methodology used is theoretical in nature and makes use of a wide bibliography to find evidence for its therapeutic effect. In essence, body percussion can be seen to lead to improvements in three areas. the Physical, as it stimulates awareness of the body, control of movement and muscular strength, coordination and balance; the Mental, as it improves concentration, memory and perception; and finally Socio-affective, as it helps to build egalitarian relationships and leads to a decrease in anxiety in social interactions. This means of therapy has several different uses and it is targeted at different groups. In the present investigation we categorise them into five main groups: individuals with neurodegenerative diseases like Alzheimer's or Parkinson's disease; individuals with learning disorders such as dyslexia or ADHD; patients affected by diseases of the spinal cord, cranial neuropathies and trauma (Neurorehabilitation); and for the treatment of addictive behavior (addiction); and depressive disorders or anxiety disorders. After thorough analysis, we have found scientific evidence that the therapeutic body percussion using the BAPNE method improves the quality of life of patients and it is an important factor in stabilizing the development of different diseases.In addition, evidence involving certain biological indicators (in control and experimental groups, and through a pre-test and post-test) show its effect on levels of stress and anxiety (reduction of cortisol), as well as improvement of social relations as a result of working as a group (increased levels of oxytocin), and improvements seen in self-esteem and in a variety of personal aspects through the Aspects of Identity questionnaire

Percusión Corporal y TDAH en el método BAPNE. Introducción metodológica

En este artículo justificamos el uso terapéutico de la percusión corporal según el método Bapne en el trastorno de Déficit de Atención e Hiperactividad TDAH. Los sujetos con este tipo de trastorno se caracterizan por presentar dificultades vinculadas a la regulación de la conducta y especialmente por tener dificultades en las funciones ejecutivas. Dicha disfunción ejecutiva pone de relieve una pobre memoria de trabajo, verbal y no verbal, dificultades en la regulación del afecto, la motivación y la excitación, dificultades para analizar una situación, para planificar y organizarse y dificultades para inhibir respuestas. Bajo el paraguas de la teoría de los comportamientos enmascaradores, estas vivencias de fracaso, dificultad y estrés quedan almacenadas en el inconsciente emocional y desembocan en la configuración de un patrón de respuesta de defensa y protección. Desde el método Bapne, sostenemos que la práctica de la percusión corporal terapéutica ayuda a reconfigurar estos patrones de respuesta habitual, favoreciendo la auto percepción de auto competencia mediante el aprendizaje entre iguales, estimulando la memoria de trabajo, la empatía, mejorando la autoestima y muy especialmente facilitando la autonomía en la atención

Evaluation of the mechanical properties of cements with fillers derived from the CO2 reduction of cement plants

This work introduces a novel method for the development of CO2 recovery systems derived from the production process of cement in order to obtain CaCO3 nanofiller in cement-based composites. Research was carried out in collaboration between the Department of Applied Science and Technology (DISAT) and the Department of Structural, Construction and Geotechnical Engineering (DISEG) of Politecnico di Torino. The objective of this method was dual. Firstly, it aimed to obtain a precipitated calcium carbonate - nanoCaCO3 - with a high degree of purity. Secondly, it aimed to optimize the characteristics of these nanoparticles e.g. additional percentages, morphology, particle size distribution or crystal phase, according to their use in cement-based composites. The synthesized nanoCaCO3 particles were subsequently added into the cementitious composites in different percentages according to the weight of the cement, in order to understand their behaviour within the cement matrix. The mechanical properties were also evaluated, both at 7 and 28 days, through three point bending and compression tests. The results of the mechanical tests showed a promising improvement in strength and toughness. This study is a first step towards developing a CO2 circular economy