Twisted Form Research Articles

Twisted holomorphic symplectic forms

We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the form is parallel. We then describe the structure of the fundamenal group of such manifolds and derive some consequences.

Advances in electrospinning: The production and application of nanofibres and nanofibrous structures

ABSTRACTThe use of electrospun nanofibres in applications such as medical products, fuel cells, photocatalysis, filtration, sensors and actuators is reviewed. Yarn production is classified into two types, namely hollow and core-shell structures; the methods used for producing the two structures for different polymers are discussed. Explanations are given for the various arrangements for producing nanofibre yarns and bundles in non-twisted or twisted forms to suit their end use. Natural and synthetic polymer products for biomedical uses and their applications in the form of polymer nanofibres are reviewed and polymeric optical fibres for use in photonic devices and optical circuits are evaluated. The production and development of nanofibrous filtration devices is explored with specific reference to water treatment and the control of air pollution. Particular attention is then given to the evaluation of different electrospinning methods for PVDF (polyvinylidene fluoride), a piezoelectric polymer widely used in sensor applications in terms of their ability to harvest more energy after agitation of the sensor and the effects of different additives on the piezoelectric properties of PVDF. Priorities for further research are then outlined.

Reinvestigation of the photoreaction of 1,4-bis(2,4,6-triphenylpyridinio)benzene: Synthesis of a diazonia derivative of hexabenzoperylene by multiple photocyclization

Abstract The photo-induced oxidative cyclization of the 1,1′-p-phenylene-bis(2,4,6-triphenylpyridinium) was reinvestigated. While mono-cyclization was claimed to be the photoproduct in a previous report, it was found that the diazonia derivative of hexabenzoperylene can be formed as the final photoproduct by four-fold cyclization. The photoreaction affords one of the two possible stereoisomers (twisted and anti forms), and the stereostructure of the product is assigned to the twisted form by 1H NMR titration study with a chiral complexing reagent and by analysis of the absorption spectrum using TD-DFT calculations. The diazonia derivative of hexabenzoperylene exhibits yellow and red luminescence in the solution and solid states respectively and possesses well-separated four-reversible one-electron reduction potentials.

The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

Let [Formula: see text] be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian [Formula: see text] and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if [Formula: see text] is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of [Formula: see text].

On Gravitational Form Factors and Transverse Spin Sum Rule

Using the light front wave functions of the scalar quark–diquark model for nucleon predicted by the soft-wall AdS/QCD, we calculate the flavor dependent gravitational form factors. We evaluate the matrix element of Pauli–Lubanski operator in this model and show that the intrinsic spin sum rule involves the higher twist form factor \({\bar{C}}\). The longitudinal momentum densities in the transverse impact parameter space are also discussed for both unpolarized and transversely polarized nucleons.

On the Hilbert scheme of degeneracy loci of twisted differential forms

We prove that, for 3 < m < n-1, the Grassmannian of m-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension n is birational to the Hilbert scheme of the degeneracy loci of m global sections of Omega(2), the twisted cotangent bundle on P^{n-1}. For 3=m<n-1 and n odd, this Grassmannian is proved to be birational to the set of Veronese surfaces parametrized by the Pfaffians of linear skew-symmetric matrices of order n.

Effects of electric field on a copper–dioxolene complex adsorbed on a gold surface

A model of a copper–dioxolene complex linked to Au(111) surface with butanethiol linker is investigated using first-principles methods. It is shown that the complex adsorbed at the surface may appear in various locally stable structural forms differing in electron charge and spin density distribution, the symmetric high spin (HS) one and the twisted low spin (LS) structure. The electric field directed perpendicular to the surface controls the amount of the charge transfer between the complex and the substrate, starting from the zero-field value of Q=+0.18|e| up to the value of Q=+0.94|e| for the field strength of E=0.5V/Å. The field modifies also the mutual stability of the two structural forms, reducing the energy gap between the more energetically stable LS twisted form and the symmetrical HS one, from a value of Δ∼0.29eV in absence of the field to Δ∼0.11eV for the field strength of E=0.35V/Å.

A "twist" on the interpretation of the multifluorescence patterns of DASPMI.

In this computational study, we describe the decay mechanism of DASPMI, providing robust and documented answers to some crucial questions of still open debates on the photophysical behavior of this cationic dye. After the initial excitation, the system evolves along a torsional motion, characterized by a quite flat potential energy surface, which crosses an intramolecular charge transfer (ICT) excited state with higher energy. A nonemissive twisted-ICT (TICT) minimum is populated, and this enhances the radiationless deactivation to the ground state. Additionally, during the twisting motion path toward the TICT minima, the system can emit in a quite wide range of angles, which should lead to a red shift of the locally excited (LE) emission and asymmetric broadening of fluorescence. This picture is fully supported by experimental evidence of the multifluorescence of DASPMI. Three twisted minima are found with different energies (namely, T1, T2, and T3). The extension of the work to charge properties shows that, in the GS, the positive charge of the molecule is mainly localized on the acceptor moiety (i.e., methyl-pyridinium), and after the excitation, the charge delocalizes over the whole molecule with a slight preference for the acceptor moiety. Because of the subsequent deactivation via twisting motions, the positive charge moves from the acceptor to the donor moiety (dimethylaminophenyl moiety) so that in TICT minima the positive charge is localized in the donor part. These large differences between charge localization in LE and TICT minima are responsible for a larger population of twisted forms in solvents of increasing polarity and the enhancement of radiationless deactivation.

Semiorthogonal decompositions for twisted grassmannians

In this article, we present semiorthogonal decompositions for twisted forms of grassmannians

Some special features of Cayley algebras, and [formula omitted], in low characteristics

Some features of Cayley algebras (or algebras of octonions) and their Lie algebras of derivations over fields of low characteristic are presented. More specifically, over fields of characteristic 7, explicit embeddings of any twisted form of the Witt algebra into the simple split Lie algebra of type G2 are given. Over fields of characteristic 3, even though the Lie algebra of derivations of a Cayley algebra is not simple, it is shown that still two Cayley algebras are isomorphic if and only if their Lie algebras of derivations are isomorphic. Finally, over fields of characteristic 2, it is shown that the Lie algebra of derivations of any Cayley algebra does not depend on the Cayley algebra as it is always isomorphic to the projective special linear Lie algebra of degree four. The twisted forms of this latter algebra are described too. Any such form is, up to isomorphism, the second derived power of the Lie algebra of skew elements relative to a symplectic involution in a central simple associative algebra of degree six.

Tunable Optical Excitations in Twisted Bilayer Graphene Form Strongly Bound Excitons

When two sheets of graphene stack in a twisted bilayer graphene (tBLG) configuration, the resulting constrained overlap between interplanar 2p orbitals produce angle-tunable electronic absorption resonances. By applying a novel combination of multiphoton transient absorption (TA) microscopy and TEM, we resolve the electronic structure and ensuing relaxation by probing resonant excitations of single tBLG domains. Strikingly, we find that the transient electronic population in resonantly excited tBLG domains is enhanced many fold, forming a major electronic relaxation bottleneck. Two-photon TA microscopy shows this bottleneck effect originates from a strongly bound, dark exciton state lying ∼0.37 eV below the 1-photon absorption resonance. This stable coexistence of strongly bound excitons alongside free-electron continuum states has not been previously observed in a metallic, 2D material.

Degeneracy loci of twisted differential forms and linear line complexes

We prove that the Hilbert scheme of degeneracy loci of pairs of global sections of Omega(2), the twisted cotangent bundle on P^(n-1), is unirational and dominated by the Grassmannian of lines in the projective space of skew-symmetric forms over a vector space of dimension n. We provide a constructive method to find the fibers of the dominant map. In classical terminology, this amounts to giving a method to realize all the pencils of linear line complexes having a prescribed set of centers. In particular, we show that the previous map is birational when n=4.

Infrared and Raman spectra, DFT-calculations and spectral assignments of 1,1,3,3,5,5-hexafluoro-1,3,5-trisilacyclohexane

The infrared and Raman spectra of 1,1,3,3,5,5-hexafluoro-1,3,5-trisilacyclohexane (c-C3H6Si3F6) as a solid powder have been recorded. The vibrational spectra reveal that the crystalline compound exists as a chair conformer with C3v symmetry at ambient temperature. Additional conformers such as twist or boat were not detected although quantum chemical calculations indicated a negligible energy difference between chair, twist and boat forms. The wavenumbers of the IR and Raman bands were measured and the assignments were initially supported by quantum chemical B3LYP/cc-pVTZ calculations in the harmonic approximation. These vibrational modes were scaled with a common factor of 0.98, and the 11 totally symmetric A1 and 16 doubly degenerate E fundamentals were assigned on the basis of the infrared and Raman intensities.An average relative deviation of ca. 2.9% between the observed and the scaled harmonic calculations was found. Additional calculations were made in the anharmonic approximation, in which the symmetry was reduced to Cs symmetry by a slight distortion of the hexagonal ring. Employing these calculations without scaling, a better agreement between the observed and calculated wavenumbers was obtained (1.5%). Further calculations, involving a twist conformer was not consistent with the spectral results, neither in terms of the number of modes nor their wavenumbers.

Synthesis, Structures, and Properties of π-Extended Double Helicene: A Combination of Planar and Nonplanar π-Systems

The synthesis, structures, and properties of a π-extended double helicene 1 are described. This double helicene 1 was synthesized by a four-fold oxidative C-H biphenylation of naphthalene followed by the Scholl reaction or via five steps including the Suzuki-Miyaura cross-coupling reaction and the Scholl reaction. Due to the two helical substructures, 1 has three isomers, i.e., two enantiomers in a twisted form [(P,P) and (M,M)] and one diastereoisomer in a meso form. X-ray crystallographic analysis of the twisted isomers (twisted-1) revealed a tightly offset packing pattern of (P,P)- and (M,M)-twisted isomers, affording a three-dimensional lamellar stacking structure. A high isomerization barrier (43.5 kcal mol(-1)) and the relative thermal stability of twisted-1 isomer over meso-1 by 0.9 kcal mol(-1) were estimated by DFT calculations. The three isomers were successfully separated by chiral HPLC and characterized by circular dichroism spectroscopy as well as by TD-DFT studies. Electronic state variation resulting from the molecular geometry difference between the two diastereoisomers (twisted-1 and meso-1) was observed by UV-vis absorption and fluorescence spectra.

A new hierarchically-structured n-dimensional covariant form of rotating equations of geophysical fluid dynamics

We introduce n-dimensional equations of geophysical fluid dynamics (GFD) valid on rotating n-dimensional manifolds. Moreover, by using straight and twisted differential forms and an auxiliary velocity field, we introduce hierarchically-structured equations of (geophysical) fluid dynamics in which the equations are split into metric-free and metric-dependent parts. For these sets of equations we provide representations in local coordinate charts and we show that they conserve potential vorticity and that Kelvin’s circulation theorem holds. As such general n-dimensional formulations do not exist in vector calculus, we provide for both covariant and vector-invariant equations a representation on a rotating coordinate frame in an Euclidean space and compare these representations. This study reveals, among others, that the prognostic variables, described by straight and twisted differential forms, are independent of both metric and orientation. This makes them perfect descriptors of the fluid’s quantities of interest, as they assign, analogously to physical measurement devices, real valued numbers to finite distances, areas, or volumes. This is not the case for prognostic variables described by (vector) proxy fields, as they depend on metric and orientation. The new structuring reveals also important geometrical features of the equations of GFD. For instance, the dimensioned differential forms display the geometric nature of the fluid’s characteristics, while the equations’ structuring illustrates how the metric-free momentum and continuity equations geometrically interact and how they are connected by the metric-dependent Hodge star and Riemannian lift. Besides this geometric insight, this structuring has also practical benefits: since equations containing only topological structure are less complicated to implement and can be integrated exactly, our results may contribute to more efficient and accurate discretizations.

Convergence of the Generalized Kähler-Ricci Flow

In this paper, we consider the convergence of the generalized Kahler-Ricci flow with semi-positive twisted form \(\theta \) on Kahler manifold \(M\). We give detailed proofs of the uniform Sobolev inequality and some uniform estimates for the metric potential and the generalized Ricci potential along the flow. Then assuming that there exists a generalized Kahler-Einstein metric, if the twisting form \(\theta \) is strictly positive at a point or \(M\) admits no nontrivial Hamiltonian holomorphic vector field, we prove that the generalized Kahler-Ricci flow must converge in \(C^\infty \) topology to a generalized Kahler-Einstein metric exponentially fast, where we get the exponential decay without using the Futaki invariant.

Versality of algebraic group actions and rational points on twisted varieties

We formalize and study several competing notions of versality for an action of a linear algebraic group on an algebraic varietyXX. Our main result is that these notions of versality are equivalent to various statements concerning rational points on twisted forms ofXX(existence of rational points, existence of a dense set of rational points, etc.). We give applications of this equivalence in both directions to study versality of group actions and rational points on algebraic varieties. We obtain similar results onpp-versality for a prime integerpp. An appendix, containing a letter from J.-P. Serre, puts the notion of versality in a historical perspective.

Note on the filtrations of the K-theory

Let $X$ be a (colimit of) smooth algebraic variety over a subfield $k$ of $\mathbf C$. Let $K_{alg}^0(X)$ (resp. $K_{top}^0(X(\mathbf C)))$ be the algebraic (resp. topological) $K$-theory of $k$ (resp. complex) vector bundles over $X$ (resp. $X(\mathbf C)))$. When $K_{alg}^0(X) \cong K_{top}^0(X(\mathbf C))$, we study the differences of its three (gamma, geometrical and topological) filtrations. In particular, we consider in the cases $X = BG$ for algebraic group $G$ over algebraically closed fields $k$, and $X = \mathbf G_k/T_k$ the twisted form of flag varieties $G/T$ for non-algebraically closed field $k$.

Exotic Twisted Equivariant Cohomology of Loop Spaces, Twisted Bismut–Chern Character and T-Duality

We define exotic twisted $S^1$-equivariant cohomology for the loop space $LZ$ of a smooth manifold $Z$ via the invariant differential forms on $LZ$ with coefficients in the (typically non-flat) holonomy line bundle of a gerbe, with differential an equivariantly flat superconnection. We introduce the twisted Bismut-Chern character form, a loop space refinement of the twisted Chern character form, which represent classes in the completed periodic exotic twisted $S^1$-equivariant cohomology of $LZ$. We establish a localisation theorem for the completed periodic exotic twisted $S^1$-equivariant cohomology for loop spaces and apply it to establish T-duality in a background flux in type II String Theory from a loop space perspective.

Forms of an affinoid disc and ramification

Let k be a complete nonarchimedean field and let X be an affinoid closed disc over k. We classify the tamely ramified twisted forms of X. Generalizing classical work of P. Russell on inseparable forms of the affine line we construct explicit families of wildly ramified forms of X. We finally compute the class group and the Grothendieck group of forms of X in certain cases.