Group F4 Research Articles

Black hole solutions to the [formula omitted]-model and their orbits (I)

In this paper we continue the program of the classification of nilpotent orbits using the approach developed in arXiv:1107.5986, within the study of black hole solutions in D=4 supergravities. Our goal in this work is to classify static, single center black hole solutions to a specific N=2 four-dimensional “magic” model, with special Kähler scalar manifold Sp(6,R)/U(3), as orbits of geodesics on the pseudo-quaternionic manifold F4(4)/[SL(2,R)×Sp′(6,R)] with respect to the action of the isometry group F4(4). Our analysis amounts to the classification of the orbits of the geodesic “velocity” vector with respect to the isotropy group H⁎=SL(2,R)×Sp′(6,R), which include a thorough classification of the nilpotent orbits associated with extremal solutions and reveals a richer structure than the one predicted by the β–γ-labels alone, based on the Kostant–Sekiguchi approach. We provide a general proof of the conjecture made in hep-th/0908.1742 which states that regular single center solutions belong to orbits with coinciding β–γ-labels. We also prove that the reverse is not true by finding distinct orbits with the same β–γ-labels, which are distinguished by suitably devised tensor classifiers. Only one of these is generated by regular solutions. Since regular static solutions only occur with nilpotent degree not exceeding 3, we only discuss representatives of these orbits in terms of black hole solutions. We prove that these representatives can be found in the form of a purely dilatonic four-charge solution (the generating solution in D=3) and this allows us to identify the orbit corresponding to the regular four-dimensional metrics. H⁎-orbits with degree of nilpotency greater than 3 are analyzed solely from a group theoretical point of view, leaving a systematic analysis of their possible interpretation in terms of static multicenter or stationary non-static solutions to a future work. We just limit ourselves to give (singular) single-center representatives of these orbits, to be possibly interpreted as singular limits of regular multicenter solutions. We provide the explicit transformations mapping the various H⁎-orbits and in particular BPS into non-BPS regular solutions showing that they in general belong to the complexification of the global symmetry group in D=3.

ON THE GEOMETRY OF THE SUPERMULTIPLET IN M-THEORY

The massless supermultiplet of 11-dimensional supergravity can be generated from the decomposition of certain representation of the exceptional Lie group F4 into those of its maximal compact subgroup Spin(9). In an earlier paper, a dynamical Kaluza–Klein origin of this observation is proposed with internal space the Cayley plane, 𝕆P2, and topological aspects are explored. In this paper we consider the geometric aspects and characterize the corresponding forms which contribute to the action as well as cohomology classes, including torsion, which contribute to the partition function. This involves constructions with bilinear forms. The compatibility with various string theories are discussed, including reduction to loop bundles in ten dimensions.

Magnetic and magnetocaloric properties of Gd1−xScxNi2 solid solutions

Magnetic and heat capacity measurements have been carried out on the polycrystalline Gd1−xScxNi2 solid solutions (0≤x≤1), which crystallize in the cubic C15 Laves phases superstructure (space group F4−3m). These solid solutions are ferromagnetic with a Curie temperature below 76K. Their Curie temperature decreases from 75.4K for GdNi2 to 13.6K for Gd0.2Sc0.8Ni2. At high temperatures, all solid solutions, except ScNi2, are Curie–Weiss paramagnets. The Debye temperature as well as phonon, conduction electron and magnetic contributions to the heat capacity have been determined from heat capacity measurements. The magnetocaloric effect has been estimated both in terms of isothermal magnetic entropy change and adiabatic temperature change for selected solid solutions in magnetic fields up to 3T.

Large reversible magnetocaloric effect due to a rather unstable antiferromagnetic ground state in Er4NiCd

Er 4 NiCd crystallizes with the Gd4RhIn type structure, space group F4¯3m, a=1333.3 pm. The nickel atoms have trigonal prismatic rare earth coordination. Condensation of the NiEr6 prisms leads to a three-dimensional network which leaves voids that are filled by regular Cd4 tetrahedra. Er4NiCd shows Curie–Weiss behavior above 50 K with TN=5.9 K. At field strength of 4 kOe a metamagnetic step is visible, together with the positive paramagnetic Curie-temperature (7.5 K) indicative for the rather unstable antiferromagnetic ground state. Therefore, a large reversible magnetocaloric effect (MCE) near the ordering temperature occurs and the values of the maximum magnetic-entropy change −ΔSMmax reach 18.3 J kg−1 K−1 for the field change of 5 T with no obvious hysteresis loss around 17 K. The corresponding RCP of 595 J kg−1 is relatively high as compared to other MCE materials in that temperature range. These results indicate that Er4NiCd could be a promising system for magnetic refrigeration at temperatures below liquid H2.

Ab initio calculations of structural, electronic, optical, and elastic properties of pure and Yb-doped InP at varying pressure

Results of ab initio calculations of structural, electronic, optical, and elastic properties of pure and Yb-doped InP at pressures between ambient and 10 GPa in the density functional theory framework, using the CASTEP module of Materials Studio 4.0, are reported. It is assumed (in agreement with the experiment) that in this range of pressures pure InP and InP:Yb crystallizes in space group F4¯3m with four formula unit in a unit cell. Obtained values of lattice constant, bulk modulus, and its pressure derivative are in good agreement with experimental values reported by different authors. Additional calculations of the overlap integrals between the ytterbium and phosphorus wave functions in the InP host confirm that the observed previously [Kaminska et al., Phys. Rev. B 81, 165209 (2010)] at pressure of above 6 GPa effect of limiting of increase in f–f intrashell transition energies with increased pressure is associated with the top of the valence band of InP crystal host approaching the energies of the f–f Yb transitions.

Synthesis and Thermoelectric Properties of Half-Heusler Zr-Ni-Sn Alloy Processed by Mechanically Alloying and Hot Pressing

Recent search for novel thermoelectric materials has revealed a new class of compounds with half-Heusler structure as good candidates for higher performance thermoelectric conversion [1-2], since the structure was first found [3]. The unit cell of the half-Heusler with a space group F4¯ 3m consists of 4 interpenetrating cubic lattices. The crystallographic sites (0,0,0) and (1/4, 1/4, 1/4) are occupied by two different transition metals, the (1/2, 1/2, 1/2) site is occupied by Sn, Sb, or Bi, and the site (3/4, 3/4, 3/4) is empty [4,5]. Candidates with this structure for the investigation would be categorized into the combination of (Ti/Zr/Hf)(Co/Ni/Pt)(Sb/Sn/Bi) [4-6].

Crystallization and preliminary X-ray crystallographic analysis of human FAF1 UBX domain.

Fas-associated factor 1 (FAF1) is a multifunctional pro-apoptotic protein that is involved in Fas-mediated apoptosis, NF-kappaB signalling and the ubiquitin-proteasome pathway. In the ubiquitin-proteasome pathway, FAF1 binds to the N domain of p97/VCP, a molecular chaperone that acts in complex with the proteasome, through its C-terminal UBX domain and inhibits the proteasomal protein-degradation process. In an effort to elucidate the structural basis of the function of FAF1 in modulating p97/VCP activity related to proteasomal protein degradation, crystallographic analysis of the FAF1 UBX domain and the p97/VCP N domain was initiated. Following the recently reported crystallization of the FAF1 UBX domain bound to the p97/VCP N domain, the unbound FAF1 UBX domain was also crystallized for purposes of structural comparison. X-ray data were collected to 3.00 A resolution and the crystals belonged to space group F4(1)32, with unit-cell parameters a = b = c = 176.40 A. The Matthews coefficient and solvent content were estimated to be 3.04 A(3) Da(-1) and 59.5%, respectively, assuming that the asymmetric unit contained two molecules of the UBX domain, which was subsequently confirmed by molecular-replacement calculations.

Dexmedetomidine suppresses the decrease in blood pressure during anesthetic induction and blunts the cardiovascular response to tracheal intubation

Study Objective To evaluate the effect of dexmedetomidine combined with fentanyl on hemodynamics. Design Prospective, double-blinded, randomized study. Setting Operating room of a university hospital. Patients 30 ASA physical status II and III patients with mild-to-moderate cardiovascular disease. Interventions Patients were assigned to one of three groups: Group D-F2 [dexmedetomidine, effect-site concentration (ESC) of fentanyl = two ng/mL]; Group F2 (placebo, ESC of fentanyl = two ng/mL), or Group F4 (placebo, ESC of fentanyl = 4 ng/mL). Measurements Dexmedetomidine (an initial dose of 1.0 μg/kg for 10 min, followed by a continuous infusion of 0.7 μg·kg –1·hr –1) or placebo saline was administered 15 minutes before anesthetic induction. Anesthesia was induced with propofol and fentanyl using a target-controlled infusion system. Hemodynamic parameters: systolic (SBP) and diastolic blood pressures (DBP), and heart rate (HR) during anesthetic induction were measured and the percent changes were calculated for both induction and intubation. Main Results After inducing anesthesia, SBP was significantly higher in Group D-F2 (127 ± 24 mmHg) than Group F2 (90 ± 20 mmHg) or Group F4 (77 ± 21 mmHg). The SBP in Groups F2 and F4 reached 160 ± 31 mmHg and 123 ± 36 mmHg, respectively, after intubation, but no significant change in SBP was noted in Group D-F2. The percent increase in SBP due to tracheal intubation in Group D-F2 was 3% ± 4% and was significantly lower than that of Group F2 (70% ± 34%) or Group F4 (45% ± 36%). Conclusion Dexmedetomidine combined with fentanyl during anesthetic induction suppresses the decrease in blood pressure due to anesthetic induction and also blunts the cardiovascular response to tracheal intubation.

Low cohomogeneity and polar actions on exceptional compact Lie groups

We study isometric Lie group actions on the compact exceptional groups E6, E7, E8, F4 and G2 endowed with a biinvariant metric. We classify polar actions on these groups. We determine all isometric actions of cohomogeneity less than three on E6, E7, F4 and all isometric actions of cohomogeneity less than 20 on E8. Moreover we determine the principal isotropy algebras for all isometric actions on G2.

${\mathbb O}P^2$ bundles in M-theory

Ramond has observed that the massless multiplet of eleven-dimensional supergravity can be generated from the decomposition of certain representation of the exceptional Lie group F4 into those of its maximal compact subgroup Spin(9). The possibility of a topological origin for this observation is investigated by studying Cayley plane, OP2, bundles over eleven-manifolds Y. The lift of the topological terms gives constraints on the cohomology of Y which are derived. Topological structures and genera on Y are related to the corresponding ones on the total space M. The latter, being 27-dimensional, might provide a candidate for `bosonic M-theory'. The discussion leads to a connection with an octonionic version of Kreck-Stolz elliptic homology theory.

Cohomological invariants: exceptional groups and spin groups

This volume concerns invariants of G-torsors with values in mod p Galois cohomology - in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology - for various simple algebraic groups G and primes p. The author determines the invariants for the exceptional groups F4 mod 3, simply connected E6 mod 3, E7 mod 3, and E8 mod 5. He also determines the invariants of Spinn mod 2 for n </= 12 and constructs some invariants of Spin14. Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of Spinn is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.

Observation of a calcium-binding site in the γ-class carbonic anhydrase fromPyrococcus horikoshii

Carbonic anhydrases are zinc-containing metalloenzymes that catalyze the interconversion of carbon dioxide and bicarbonate. Three crystal structures of gamma-class carbonic anhydrase (one of which is bound to a bicarbonate molecule) from the aerobic OT3 strain of the hyperthermophilic archeon Pyrococcus horikoshii have been solved by molecular replacement in space group F4(1)32. The asymmetric unit contains a monomer of 173 amino acids and a catalytic Zn2+ ion. The protein fold is a regular prism formed by a left-handed beta-helix, similar to previously reported structures. The active-site Zn2+ ion located at the interface between the two monomers is bound to three histidyl residues and a water molecule in a tetrahedral fashion. In addition to the 20 beta-strands comprising the beta-helix, there is also a long C-terminal alpha-helix. For the first time, Ca2+ ions have been observed in addition to the catalytic Zn2+ ion. It is hypothesized that Tyr159 (which corresponds to the catalytically important Asn202 in previously reported structures) utilizes C-H...pi interactions to fulfill its functions. This study may shed light on the catalytic mechanism of the enzyme and throw open new questions on the mechanism of product removal in carbonic anhydrases.

Mapping the geometry of the F4 group

In this paper, we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 Hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2 = F4/Spin(9), the octonionic projective plane, these results are a prerequisite for the study of E6, of which F4 is a (maximal) subgroup.

Crystal growth of argyrodite-type phases Cu8–xGeS6−xIx and Cu8–xGeSe6−xIx (0⩽x⩽0.8)

Abstract The growth of single crystalline argyrodites of type Cu 8− x GeX 6− x Y x ( X =S, Se; Y =I) is reported. These materials undergo solid–solid phase transitions at temperatures ranging from 30 to 90 °C. In the high temperature phase, Cu 8 GeS 6 crystallizes in the cubic space group F4¯3m. In the low temperature phase, the compound is present in the orthorhombic space group Pmn2 1 . Cu 8 GeSe 6 appears exclusively in the hexagonal space groups P6 3 mc or P6 3 cm, respectively. Single crystals of these argyrodites were obtained by chemical vapor transport in a temperature gradient Δ T =980−950 and Δ T =700−620 °C for sulfides and selenides, respectively. As a result of the growth process, the high temperature phase remains stable even at ambient temperature by incorporation of the transport agent iodine during the growth process. As determined by energy dispersive X-ray analysis (EDAX), the composition of the sulfide crystals grown ranges from Cu 8 GeS 6 to Cu 7.16 GeS 5.16 I 0.84 . The selenide crystallizes as Cu 7.69 GeSe 5.69 I 0.31 . In contrast, the solid state reaction of the elements Cu, Ge and X produces a material in the low temperature modification with an ideal composition of Cu 8 GeX 6 .

Spectroscopy and Lasing of Yb-Doped &lt;formula formulatype="inline"&gt; &lt;tex&gt;${\hbox {NaY}}{({\hbox {WO}}_{4})}_{2}$&lt;/tex&gt; &lt;/formula&gt;: Tunable and Femtosecond Mode-Locked Laser Operation

Tetragonal (space group f4 macr) single crystals of NaY(WO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> doped with Yb to a density of 4.52 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> have been employed as laser active materials for the 1-mum spectral range, operating at room temperature. Using Ti:sapphire laser pumping, slope efficiencies as high as 74.6% were achieved without special cooling for the pi-polarization. The Yb-laser was continuously tunable from 1003.7 to 1073.0 nm with a birefringent filter. Pulses as short as 53 fs were obtained at 1035 nm by SESAM passive mode-locking with intracavity dispersion compensation and additional extracavity pulse compression using analogous prism pairs. Experimental data on the spectroscopic properties of Yb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> in the 5-300 K temperature range and the room temperature optical properties of this novel Yb-host is also presented.

Inequality of Quenched and High Temperature Structure of Lithium Deficient LiMn2O4.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Quasirecognizability by the Set of Element Orders for Groups 3 D 4(q) and F 4(q), for q Odd

It is proved that if L is one of the simple groups 3D4(q) or F4(q), where q is odd, and G is a finite group with the set of element orders as in L, then the derived subgroup of G/F(G) is isomorphic to L and the factor group G/G′ is a cyclic {2, 3}-group.

Inequality of quenched and high temperature structure of lithium deficient LiMn 2O 4

Structural characterization of the new low temperature polymorph of the lithium-deficient lithium–manganese spinel, synthesized and quenched from 1073 K has been obtained by Rietveld structure refinements of X-ray powder diffraction data recorded using synchrotron radiation. A slight lithium ions deficiency causes formation of the tetragonal phase provided that the samples obtained at high temperature are rapidly quenched in the solid CO 2. The new phase has a tetragonally distorted spinel structure at 140 K with a space group F4 1 /ddm, unit cells of a = 8.33180(6) Å and c = 8.08617(7) Å. On heating, at 280 K, the tetragonal phase transforms to cubic spinel structure ( Fd3m) and it remains cubic up to 1163 K.

Thermoelectric properties of ScCoSb, ScNi 0.86Sb and MgNiSb compounds

Thermoelectric properties (from 240 up to 380 K) of the new LiGaGe-type ScCoSb, MgAgAs-type ScNi 0.86Sb and known MgAgAs-type MgNiSb are reported. The crystallographic data for the new ScCoSb, ScNi 0.86Sb and InNi 2-type ScCu 0.56Sb compounds are reported, too. The ScCoSb compound ( a = 0.4255(1) nm, c = 0.6800(1) nm) crystallizes in the LiGaGe-type structure (space group P6 3 mc, No. 186). The ScNi 0.86Sb compound ( a = 0.60496(8) nm) crystallizes in the MgAgAs-type structure (space group F4 b3 m, No. 216) and ScCu 0.56Sb ( a = 0.42251(8) nm, c = 0.6835(1) nm) crystallizes in the InNi 2-type structure (space group P6 3/ mmc, No. 194). The Seebeck coefficients increase with increasing temperature from 240 up to 380 K for ScCoSb ( S = 16, …, 25 μV/K) and MgNiSb ( S = 2.1, …, 2.9 μV/K). The ScNi 0.86Sb compound shows a change of the type of conductivity from semi-metal to the semiconductor at 290–300 K. Due to this, the temperature dependences of the Seebeck coefficient and electrical resistivity have a maximum at 290–300 K, but that of the thermal conductivity has a minimum at 290 K. The Seebeck coefficient of ScNi 0.86Sb reaches 42 μV/K at 300 K. The ScCoSb has the best ZT parameter from present compounds: ZT = 0.009 at 380 K.

Order-disordered structure and magnetic properties of Li0.5Fe2.5−xRhxO4

Li 0.5 Fe 2.5 − x Rh x O 4 (x=0.25–1.50) has been studied by Mössbauer spectroscopy, superconducting quantum interference device magnetometry, and x-ray diffraction. The crystals are found to be a cubic spinel structure and have been classified into two different sets by crystallographic symmetry, the space group Fd3m for x=0.25–1.25 and the space group F4¯3m for x=1.50, respectively. The migration of Li ion has been confirmed by x-ray patterns and the results of Mössbauer analysis. The saturated magnetic moment measured at 4.2K and Mössbauer spectra taken at various temperatures with 6.0T applied field show that the spin structure of Li0.5Fe2.5−xRhxO4 has the collinear Néel model.