Mathematical Magic: A Study of Number Puzzles

Within this paper, we will briefly review the history of a collection of number puzzles which take the shape of squares, polygons, and polyhedra in both modular and nonmodular arithmetic. Among other results, we develop construction techniques for solutions of both Modulo and regular Magic Squares. For other polygons in nonmodular arithmetic, specifically of order 3, we present a proof of why there are only four Magic Triangles using linear algebra, disprove the existence of the Magic Tetrahedron in two ways, and utilizing the infamous 3-SUM combinatorics problem we disprove the existence of the Magic Octahedron

Tuning the Lewis Acidity of Boranes in Frustrated Lewis Pair Chemistry: Implications for the Hydrogenation of Electron-Poor Alkenes

An analysis of the metal-free reduction of electron deficient olefins by frustrated Lewis pairs indicates that the rate-determining step might be either the heterolytic cleavage of H2 to form an -onium borohydride salt, or the subsequent transfer of the hydride moiety to the substrate following a Michael-type addition reaction. While the use of strong Lewis acids such as B(C6F5)3 facilitates the first of these processes, hydride transfer to the olefin should be contrarily favoured by the use of weak Lewis acids which, for this very same reason, might be unable to promote the prior H2 split. After systematic testing of several boranes of different Lewis acidity (assessed by using the Childs’ method) and steric demand, an optimal situation that employs tris(2,4,6-trifluorophenyl)borane was reached. Mixtures of this borane with 1,4-diazabicyclo[2.2.2]octane (DABCO) exhibited excellent catalytic activity for the hydrogenation of alkylidene malonates. In fact, this transformation could be achieved under milder conditions than those we reported previously. Moreover, the reaction scope could be expanded to other electron deficient olefins containing esters, sulfones or nitro functionalities as electron-withdrawing substituents

A closer look at prion strains: characterization and important implications

Prions are infectious proteins that are responsible for transmissible spongiform encephalopathies (TSEs) and consist primarily of scrapie prion protein (PrPSc), a pathogenic isoform of the host-encoded cellular prion protein (PrPC). The absence of nucleic acids as essential components of the infectious prions is the most striking feature associated to these diseases. Additionally, different prion strains have been isolated from animal diseases despite the lack of DNA or RNA molecules. Mounting evidence suggests that prion-strain-specific features segregate with different PrPSc conformational and aggregation states. Strains are of practical relevance in prion diseases as they can drastically differ in many aspects, such as incubation period, PrPSc biochemical profile (e.g., electrophoretic mobility and glycoform ratio) and distribution of brain lesions. Importantly, such different features are maintained after inoculation of a prion strain into genetically identical hosts and are relatively stable across serial passages. This review focuses on the characterization of prion strains and on the wide range of important implications that the study of prion strains involves

Making use of geometrical invariants in black hole collisions

We consider curvature invariants in the context of black hole collision simulations. In particular, we propose a simple and elegant combination of the Weyl invariants I and J, the {\sl speciality index} ${\cal S}$. In the context of black hole perturbations $\cal S$ provides a measure of the size of the distortions from an ideal Kerr black hole spacetime. Explicit calculations in well-known examples of axisymmetric black hole collisions demonstrate that this quantity may serve as a useful tool for predicting in which cases perturbative dynamics provide an accurate estimate of the radiation waveform and energy. This makes ${\cal S}$ particularly suited to studying the transition from nonlinear to linear dynamics and for invariant interpretation of numerical results.Comment: 4 pages, 3 eps figures, Revte

Efecto de la alimentación den diferentes horas del día sobre el comportamiento productivo de conejos en crecimiento

The objective was to evaluate the effect of different feeding times on the productive performance of growing rabbits. We worked with 90 rabbits between males and females, races New Zealand with an average weight of 434g. The treatments were: T0 = power (day and night), T1 = 7pm -7am power supply and T2 = 7:00 a.m. -7pm; The diets were formulated containing 18% protein and digestible energy level 2,500kcal / Kg. Significant difference (P <0.01) feed intake was found, live weight gain, feed conversion and production costs in males and females in the tratamientoT1 COA (8727.24), IP (967.1667 ± 1.124 ab), CA (3.8), CP (S / .0.60) in males and females T1COA (8694.20), IP (956,667 ± 2,104 b), CA (3.5) and CP (S / .0.65) with respect to T0 results show treatments T2.Los the T1 was optimal for increasing live weight of male and female rabbits.El objetivo fue evaluar el efecto de diferentes horas de alimentación sobre el comportamiento productivo de conejos en crecimiento. Se trabajó con 90 conejos entre machos y hembras, de las razas Nueva Zelanda con peso promedio 434g. Los tratamientos fueron: T0= alimentación (día y noche), T1= alimentación 7pm -7am y T2= alimentación 7 am -7pm; La dietas se formularon con contenido de proteína de 18% y nivel de energía digestible de 2,500kcal/Kg. Se encontró diferencia significativas (P< 0.01) de consumo de alimento, incremento de peso vivo, conversión alimenticia y costos de producción en machos y hembras en el tratamientoT1 COA (8727.24), IP (967.1667 ± 1.124 ab), CA (3.8), CP (S/.0.60) en machos y en hembras T1COA (8694.20), IP (956.667±2.104 ab), CA (3.5) y CP (S/.0.65), con respecto a los tratamientos T0 y T2.Los resultados evidencian que el T1 fue óptimo para el incremento de peso vivo de conejos machos y hembras

Ni(II) Precatalysts Enable Thioetherification of (Hetero)Aryl Halides and Tosylates and Tandem C−S/C−N Couplings

Ni-catalyzed C−S cross-coupling reactions have received less attention compared with other C-heteroatom couplings. Most reported examples comprise the thioetherification of most reactive aryl iodides with aromatic thiols. The use of C−O electrophiles in this context is almost uncharted. Here, we describe that preformed Ni(II) precatalysts of the type NiCl(allyl)(PMe2Ar’) (Ar’=terphenyl group) efficiently couple a wide range of (hetero)aryl halides, including challenging aryl chlorides, with a variety of aromatic and aliphatic thiols. Aryl and alkenyl tosylates are also well tolerated, demonstrating, for the first time, to be competent electrophilic partners in Ni-catalyzed C−S bond formation. The chemoselective functionalization of the C−I bond in the presence of a C−Cl bond allows for designing site-selective tandem C−S/C−N couplings. The formation of the two C-heteroatom bonds takes place in a single operation and represents a rare example of dual electrophile/nucleophile chemoselective process.We thank FEDER/Ministerio de Ciencia, Innovación y Universi dades-Agencia Estatal de Investigación (Grant CTQ2017-82893-C2-2-R) and US/FEDER/JUNTA, UE (Grant, US126226) for finan cial suppor

Reproductive biology of Polioptila lembeyei (Aves: Polioptilidae) in the Siboney-Juticí Ecological Reserve, Santiago de Cuba, Cuba

Se estudió la biología reproductiva de Polioptila lembeyei en la Reserva Ecológica Siboney-Juticí, Santiago de Cuba, Cuba durante los años 2006 y 2007 en seis formaciones vegetales. Se describieron aspectos de su reproducción en términos de cronología reproductiva, tamaño de puesta, duración del período de incubación, permanencia de los polluelos en el nido, morfometría de nidos y huevos, y caracterización del sitio de nidificación en cuanto a la altura de los nidos y especie y altura de las plantas utilizadas como sitio de nidificación. Se localizaron 89 nidos durante las dos temporadas reproductivas, 43 en el año 2006 y 46 en el 2007. El período reproductivo se extendió desde finales de marzo hasta julio, abarcando 129 días en el año 2006 y 122 días durante el año 2007. Las nidadas tuvieron una duración de 36–56 días (construcción 8,6 ± 2,8 días, puesta 8,6 ± 2,7 días, incubación de 14,0 ± 1,2 días y permanencia de los pichones en el nido 14,5 ± 1,0 días). De los 45 nidos examinados el tamaño de puesta modal fue de tres huevos (88,9 %), encontrándose también nidadas de dos (6,7 %) y cuatro huevos (4,4 %). De 38 nidos con huevos para ambas temporadas, 15 nidos produjeron pichones (32 pichones en el 2006 y 20 pichones en el 2007) y solo tres nidos durante el 2006 (37,5 %) lograron producir volantones, los cuales salieron con éxito del nido. La planta más utilizada como sitio de nidificación fue Acacia macracantha (80 % de los nidos detectados), aunque también se hallaron nidos en otras ocho especies de plantas. Las alturas de ubicación del nido fue de 2,7 ± 1,5 m (n = 82; rango 0,3–6,4 m) y la distancia del nido al dosel de la planta utilizada como sustrato fue de 1,1 ± 0,9 m (n = 80; rango 0,1–5,4 m).The reproductive biology of Polioptila lembeyei was studied in six vegetation types during the years 2006 and 2007 in the Siboney-Juticí Ecological Reserve, Santiago de Cuba, Cuba. Breeding aspects including reproductive chronology, clutch size, incubation length, nestling period, egg and nest morphometrics, and aspects of the nesting site (nest height, plant species, and plant height) were described. Eighty-nine nests were found during both reproductive seasons, 43 in 2006 and 46 in 2007. The reproductive period occurred from late March to July for 129 days in 2006 and 122 days in 2007. The length of the nesting period was 36–56 days (nest construction 8.6 ± 2.8 days, laying 8.6 ± 2.7 days, incubation 14.0 ± 1.2 days, and nestling period 14.5 ± 1.0 days). Of the 45 nests examined, modal clutch size was three eggs (88.9 %), although nests with two (6.7 %) and four eggs (4.4 %) also occurred. Of 38 clutches in both seasons, 15 of them produced chicks (32 chicks in the 2006 and 20 chicks in the 2007) and only three nests in the 2006 season (37.5 %) produced fledglings. Acacia macracantha was the plant species most used as nesting substrate (80 % of detected nests) although nests were also found in eight other plant species. Nest heights were 2,7 ± 1,5 m (n = 82; range 0.3–6.4 m) and the distance from nest to the canopy of the substrate plant was 1.1 ± 0.9 m (n = 80; range 0.1–5.4 m)

Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars $\psi_4$ and $\psi_0$, which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials $\Psi$ in outgoing or ingoing {\it radiation gauges}. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e $\psi_4$ and $\psi_0$. We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.Comment: 6 Pages, Revtex

Preparation and degradation of rhodium and iridium diolefin catalysts for the acceptorless and base-free dehydrogenation of secondary alcohols

Rhodium and iridium diolefin catalysts for the acceptorless and base-free dehydrogenation of secondary alcohols have been prepared, and their degradation has been investigated, during the study of the reactivity of the dimers [M(µ-Cl)(I4-C8H12)]2 (M = Rh (1), Ir (2)) and [M(µ-OH)(I4-C8H12)]2 (M = Rh (3), Ir (4)) with 1, 3-bis(6'-methyl-2'-pyridylimino)isoindoline (HBMePHI). Complex 1 reacts with HBMePHI, in dichloromethane, to afford equilibrium mixtures of 1, the mononuclear derivative RhCl(I4-C8H12){¿1-Npy-(HBMePHI)} (5), and the binuclear species [RhCl(I4-C8H12)]2{µ-Npy, Npy-(HBMePHI)} (6). Under the same conditions, complex 2 affords the iridium counterparts IrCl(I4-C8H12){¿1-Npy-(HBMePHI)} (7) and [IrCl(I4-C8H12)]2{µ-Npy, Npy-(HBMePHI)} (8). In contrast to chloride, one of the hydroxide groups of 3 and 4 promotes the deprotonation of HBMePHI to give [M(I4-C8H12)]2(µ-OH){µ-Npy, Niso-(BMePHI)} (M = Rh (9), Ir (10)), which are efficient precatalysts for the acceptorless and base-free dehydrogenation of secondary alcohols. In the presence of KOtBu, the [BMePHI]- ligand undergoes three different degradations: Alcoholysis of an exocyclic isoindoline-N double bond, alcoholysis of a pyridyl-N bond, and opening of the five-membered ring of the isoindoline core.