53,717 research outputs found
Complexifications of local actions and the Bergman metric
No full textLet act by biholomorphisms on a Stein manifold
which admits the Bergman metric.
We show that can be regarded as a -invariant domain
in a ``universal" complex manifold on which the
complexification of acts.
The analogous result holds for actions
of a larger class of real Lie groups containing, e.g., abelian
and certain nilpotent ones. For holomorphic actions of such groups on
Stein manifolds, necessary and sufficient conditions
for the existence of are given
G. E. Müller: Die Gesichtspunkte und die Tatsachen der psychophysischen Methodik. Ergebnisse der Physiologie von G. Asher und K. Spiro. II (2), S. 1-244. Wiesbaden 1904
No full textG. E. MÜLLER: DIE GESICHTSPUNKTE UND DIE TATSACHEN DER PSYCHOPHYSISCHEN METHODIK. ERGEBNISSE DER PHYSIOLOGIE VON G. ASHER UND K. SPIRO. II (2), S. 1-244. WIESBADEN 1904
Zeitschrift für Psychologie und Physiologie der Sinnesorgane (-)
Zeitschrift für Psychologie und Physiologie der Sinnesorgane (40) (a0001)
G. E. Müller: Die Gesichtspunkte und die Tatsachen der psychophysischen Methodik. Ergebnisse der Physiologie von G. Asher und K. Spiro. II (2), S. 1-244. Wiesbaden 1904 (40) (p0108
Lorentzian manifolds with shearfree congruences and Kähler-Sasaki geometry
No full textWe study Lorentzian manifolds (M,g) of dimension n≥4, equipped with a maximally twisting shearfree null vector field p, for which the leaf space S=M/{exptp} is a smooth manifold. If n=2k, the quotient S=M/{exptp} is naturally equipped with a subconformal structure of contact type and, in the most interesting cases, it is a regular Sasaki manifold projecting onto a quantisable Kähler manifold of real dimension 2k−2. Going backwards through this line of ideas, for any quantisable Kähler manifold with associated Sasaki manifold S, we give the local description of all Lorentzian metrics g on the total spaces M of A-bundles π:M→S, A=S1,R, such that the generator of the group action is a maximally twisting shearfree g-null vector field p. We also prove that on any such Lorentzian manifold (M,g) there exists a non-trivial generalised electromagnetic plane wave having p as propagating direction field, a result that can be considered as a generalisation of the classical 4-dimensional Robinson Theorem. We finally construct a 2-parametric family of Einstein metrics on a trivial bundle M=R×S for any prescribed value of the Einstein constant. If dimM=4, the Ricci flat metrics obtained in this way are the well-known Taub-NUT metrics
Steepest descent curves of convex functions on surfaces of constant curvature
No full textLet S be a complete surface of constant curvature K = +/- 1, i.e. S^2 or H^2, and D \subset S a bounded convex subset. If S = S^2, assume also diameter(D) < \pi/2. It is proved that the length of any steepest descent curve of a quasi-convex function in D is less than or equal to the perimeter of D. This upper bound is actually proved for the class of G-curves, a family of curves that naturally includes all steepest descent curves. In case S = S^2, it is also proved the existence of G-curves, whose length is equal to the perimeter of their convex hull, showing that the above estimate is indeed optimal. The results generalize theorems by Manselli and Pucci on steepest descent curves in the Euclidean plane
Construction, Characterization, and Properties of Poly(iminofuran-spiro-oxindole)s through Catalyst-Free Multicomponent Spiropolymerization of Diisocyanides, Activated Alkynes, and Bis-isatins
No full textSpiropolymers built from monomers without spirocyclic
structures
have garnered significant academic interest and hold substantial technological
value. However, their construction still remains a challenging project,
primarily due to limited polymerization methods. Herein, we introduce
a novel multicomponent spiropolymerization for synthesizing poly(iminofuran-spiro-oxindole)s
from diisocyanides, activated alkynes, and bis-isatins without the
use of catalyst, even under mild conditions. The common natural product
isatin, a vital feedstock in the dye industry and pharmaceutical fields,
has been elegantly and rationally employed to construct spiropolymers.
The resultant spiropolymers demonstrate favorable solubility, excellent
thermal stability, satisfactory isolated yields (up to 92.6%), and
high molecular weights (up to 56800 g/mol). The experimental data
and theoretical calculations reveal that only the carbonyl group located
at position 3 of isatin is involved in the formation of spiropolymers.
Notably, despite lacking conventional fluorophores, the prepared poly(iminofuran-spiro-oxindole)
displays both clusterization-triggered emission and aggregation-enhanced
emission properties. Intriguingly, the photoluminescence can be quenched
by both ferrous and ferric ions efficiently in an organic solution
and only ferric ions exclusively in an organic/water mixture. It is
highly anticipated that this instructive work will open a new avenue
of spiropolymer construction and contribute to expanding diverse applications
New spiro-functionalized poly(fluorene)s: synthesis and properties
No full textThe synthesis of several new spirocycloalkane functionalized polyfluorenes is described. Poly[2,7-(9,9-dioetylfluorene)-alt-2',7'-spiro(cyclohexane-1,9'-fluorene)] (PH), poly[2,7-(9,9-dioctylfluorene)-co-2,7'-spiro(cyclohexane-1,9'-fluorene)] (PF2), poly (2',7'-bis[(9,9-dioctylfluoren-2-yl)]-spiro(cyclohexane-1,9'-fluorene)-7,7-diyl] (PF3), poly[2,7-(9,9-dioctylfluorene)-alt-2',7'-spiro(cyclopropane-1,9'-fluorene)] (PF4) and poly [2,7- (9,9-dioctylfluorene)-co-2',7'-spiro(cyclopropane-1,9'-fluorene)] (PF5) were synthesized by Pd(O) and Ni(O) mediated coupling reactions. All polymers were characterized by NMR, UV-vis, DSC-TGA and PL. Efficient prevention of interchain interactions by the spirocyclohexane moieties guarantees pure blue emission from pristine PF1-3 as revealed by solid state PL spectra. On the other hand, solid state PL spectra of PF4 and PF5 are characterized by an additional emission band in the green region. Thermal annealing on PF1-3 at 150degreesC under nitrogen atmosphere does not cause any substantial changes in their solid state PL spectra, whereas after carrying out the same treatment for 20 h at 110 degreesC under air the polymers show a low-energy emissionbandin the green region which is presumably brought about by chemical modifications
Six-Dimensional Nearly Kaehler Manifolds of Cohomogeneity One (II)
No full textLet M be a six dimensional manifold, endowed with a cohomogeneity one action of G= SU_2 X SU_2, and M_reg \subset M its subset of regular points. We show that M_reg admits a smooth, 2-parameter family of G-invariant, non-isometric strict nearly Kaehler structures and that a 1-parameter subfamily of such structures smoothly extend over a singular orbit of type S^3. This determines a new class of examples of nearly Kaehler structures on TS^3. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAM
Synthesis and Ring Transformation of Oxygen and Nitrogen Spiro Bisheterocycles
No full textA facile and rapid access to bridgehead oxygen-and nitrogen-containing spiro bisheterocycles is reported. It involves a one-pot spiro-to-spiro ring transformation of the key spiro[chromanone-hydantoin] compounds into new substituted spiro [hydantoin-diazole], spiro [hydantoin-isoxazole], spiro [hydantoin-diazepine], spiro [hydantoinoxazepine], and spiro [hydantoin-benzodiazepine] upon reaction with appropriate bisnucleophilic agents. The hydantoin cycle is preserved during these chemical reactions affording the spiro bisheterocycles in optimal yields (42-71%). This relevant spiro-to-spiro ring transformation was confirmed by NMR and single-crystal X-ray diffraction studies
Recent Advances in the Synthesis of Spiro‐β‐Lactams and Spiro‐δ‐Lactams
No full textSpirocyclic molecules are widely recognized
for their complex three-dimensional features
and structural rigidity. Among this class of molecules,
the spiro-lactams subclass stands out, being extensively
explored due to its bioactivity and utility in a
variety of scientific fields such as drug design and
organic synthesis. Given the recognition of spirocyclic
lactams’ broad potential, several efforts have
been engaged on the pursuit of new synthetic
strategies towards these molecules. The present review
gathers advances on the synthesis of both spiro-
β-lactams (spiroazetidin-2-ones) and spiro-δ-lactams
(spiropiperidon-2-ones) reported since 2015. The
work is divided into two distinct parts, each one
dedicated to one of these types of spiro-lactam, with
the approach used for building the spirocyclic system
being extensively discussed, according to the method’s
scope, efficiency, selectivity, and reaction mechanism
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