Twisted Form Research Articles

Twisted Pfister forms

Let F be a field of characteristic \neq 2 . In this paper we investigate quadratic forms \varphi over F which are anisotropic and of dimension 2^n, n\geq 2 , such that in the Witt ring WF they can be written in the form \varphi=\sigma -\pi where \sigma and \pi are anisotropic n - resp. m -fold Pfister forms, 1\leq m <n . We call these forms twisted Pfister forms. Forms of this type with m=n-1 are of great importance in the study of so-called good forms of height 2, and such forms with m=1 also appear in Izhboldin's recent proof of the existence of n -fold Pfister forms \tau over suitable fields F, n\geq 3 , for which the function field F(\tau ) is not excellent over F . We first derive some elementary properties and try to give alternative characterizations of twisted Pfister forms. We also compute the Witt kernel W(F(\varphi )/F) of a twisted Pfister form \varphi . Our main focus, however, will be the study of the following problems: For which forms \psi does a twisted Pfister form \varphi become isotropic over F(\psi ) ? Which forms \psi are equivalent to \varphi (i.e., the function fields F(\varphi) and F(\psi ) are place-equivalent over F )? We also investigate how such twisted Pfister forms behave over the function field of a Pfister form of the same dimension which then leads to a generalization of the result of Izhboldin mentioned above.

Density Functional Theory Studies on Sulfur−Nitrogen Species

Density functional theory (DFT) calculations on SNS, S2N2, and S4N2 are reported. Both local and gradient-corrected nonlocal density functionals are used with moderate and large basis sets. The relative energies, structural parameters, and vibrational frequencies are reported for each molecule and compared with the experimental and theoretical data available in the literature. For S2N2, DFT results predicted the order of stability of the three low-energy structures as linear chain < pairwise ring < alternate ring in contrast to the MP2 results but in agreement with MRCI results. For S4N2 the order of stability is found to be (1,3) isomer < twisted form of (1,4) isomer < chair form of (1,4) isomer. We discuss identification of experimentally observed infrared absorption peaks of S2N2 and S4N2.

Synthesis and Biological Activities of New Conformationally Restricted Analogues of (−)-Indolactam-V: Elucidation of the Biologically Active Conformation of the Tumor-Promoting Teleocidins

The tumor-promoting teleocidins and their core structure (−)-indolactam-V (1) exist in two stable conformers in solution at room temperature. The cis amide assumes a twist conformation while the trans amide exists in a sofa form. In order to identify the biologically active conformation of the teleocidins, we have synthesized new twist-restricted analogues 5a and 6 based on an aza-Claisen rearrangement of (−)-N13-desmethyl-N13-allylindolactam-V (3) and a sofa-restricted analogue, (−)-5-methylindolactam-V (22). The activities of these new compounds were evaluated in three in vitro bioassays associated with in vivo tumor-promoting activity: binding to the protein kinase C regulatory domain, induction of the Epstein−Barr virus early antigen, and stimulation of radioactive inorganic phosphate incorporation into phospholipids of HeLa cells. These three biological activities correlated well for each derivative. Twist-restricted analogues 5a and 6 showed significant activities in the three assays, comparable to 1 itself. In contrast, sofa-restricted 22 showed little activity related to tumor promotion. Introduction of a prenyl group into position 7 or 18 of 5a and 6 significantly enhanced the activity while sofa-restricted (−)-5-prenylindolactam-V (23) showed only very weak activity. These results indicate that the active conformation of the teleocidins and 1 is close to the twist form. This is the first evidence bearing on the active conformation of the teleocidins based on conformationally restricted analogues with an intact indolactam skeleton and is in accord with conclusions reported for benzolactams, analogues without the pyrrole moiety. This study also describes the synthesis of new biologically active compounds (26a, 26b, 28) based on inactive (+)-epiindolactam-V (24), involving a further application of the aza-Claisen rearrangement. Bridge formation between positions 5 and 13 of indolactam derivatives represents a particularly effective analogue design strategy, allowing for the remote control of the conformation of this ring system and for the introduction of a wide range of structural variations, as required for the development of new protein kinase C activators with high isozyme selectivity.

Self-assembly of frame structures. 10. Stereochemistry of 2,5-dioxabicyclo [2.2.1]heptane-3,6-digne

By optimization of the geometry of 2, 5-dioxabicyclo[2. 2.1]heptane-3.6-dione (1) with an ab initio (RHF/6-31 G') calculation, we have found that a single synchro(+, +)-twist form (A) corresponds to the (1 R,4R)-enantiomer (the dihedral angles of the lactone bridges areϕ0 = 2.6°). According to MM2(91) and MM3(92) calculations, (1R,4R)-1 exists as the s-ynchro(+, +)-A-twist (ϕ0 = 3.9°) and the synchro(-, -)-B-twist (ϕ = -3.8°) forms, respectively. Investigating the torsional energy surface of the dilactone 1 (MM2(91)), we found only the (1R,4R,P)-diastereomeric form (A), which is stabilized compared with the (1R,4P,M) form (B) (probably as a result of the more preferred dipole-dipole interaction of the carbonyl groups). According to the calculated puckering coordinates, the five-membered and six-membered moieties of the bicycle 1 are flattened compared with norbornane.

Euler and Pontrjagin currents of a section of a compactified real bundle

The canonical family of Thom forms τ s for 0 < s < ∞ constructed by Harvey and Lawson on an oriented real vector bundle V → X with metric connection D v is shown to have an extension to the bundle of real projective spaces, P( R ⊕ V) → X , which compactifies V in the fibre directions. The current limit as r → ∞ and s → 0 of the smooth transgression formula τ r − τ s = dσ r, s is the current equation x ̃ (D v) + [P(V)] Res − [X] = dσ ∞,0 on P( R ⊕ V) . Here σ ∞,0 is an L loc 1 current on P( R ⊕ V) and [ X] is the current of integration over the zero section of V. If the rank of V is even, x ̃ (D v) is the twisted extension to P( R ⊕ V) of the Chern-Euler form of the connection D v on V, [ P( V)] integrates densities over the nonorientable submanifold P( V) of P( R ⊕ V) and Res is a smooth twisted form on P( V). If the rank of V is odd, x ̃ (D v) ≡ 0 , [ P( V)] is the current of integration over P( V) and Res is a smooth form on P( V). This construction can be pulled back to X by an atomic section ν:X → P( R ⊕ V) satisfying an appropriate orientability hypothesis to obtain a current equation on X relating the zero and pole sets of ν to the topology of the bundle. Applications to the differential topology of maps into spheres and real projective spaces are discussed.

Conformational analysis of 3-deoxy-3-nitroheptoseptanosides by molecular mechanics (MM2) and theoretical 3JHH calculation

Molecular mechanics (MM2) calculations were performed on conformers of a series of stereoisomeric methyl 5,7- O-benzylidene-3- deoxy-3-nitro- α- d-heptoseptanosides. The lowest-energy conformations are twist forms derived from the regular 5 C 1,2 and O C 3,4 chairs. The data obtained for the steric energies and the theoretically calculated 3 J H, H coupling constants of the compounds are consistent with experimental observations on the synthetic products.

Synthesis and biological activities of new conformationally fixed analogues of (−)-indolactam-V, the core structure of tumor-promoting teleocidins

Abstract (−)-Indolactam-V ( 1 ) exists as two stable conformers, the twist and the sofa form, in solution at room temperature. 3-Aza-Cope rearrangement of (−)- N 13 -desmethyl- N 13 -allylindolactam-V ( 5 ) gave new conformationally restricted analogues ( 2a and 3 ) along with a normal rearrangement product ( 7 ). Both 2a and 3 , whose fixed conformation was the twist form, showed significant biological activities related to tumor promotion.

Automorphism group schemes of basic matrix invariants

For 3 ⩽ k &gt; n , let E k ( X ) 3 \leqslant k &gt; n,\quad {\text {let}}\quad {E_k}(X) be the polynomial in n 2 {n^2} variables defined by det ( X + λ I ) = ∑ E k ( X ) λ n − k {\text {det}}(X + \lambda I) = \sum {{E_k}(X){\lambda ^{n - k}}} . Let R R be a ring containing a field of characteristic p ⩾ 0 p \geqslant 0 . If p p does not divide n − k + 1 n - k + 1 , the invertible linear transformations on matrices preserving E k ( X ) {E_k}(X) up to scalars are (in essence) just the obvious ones arising from scaling, similarities, and transposition. If the power p s {p^s} dividing n − k + 1 n - k + 1 is greater than k k , then we have these elements times maps of the form X ↦ X + f ( X ) I X \mapsto X + f(X)I . When smaller powers p s {p^s} divide n − k + 1 n - k + 1 , the group scheme is like the first with an infinitesimal part of the second. One corollary is that every division algebra of finite dimension n 2 &gt; 4 {n^2} &gt; 4 over its center carries a canonical cubic form that determines it up to antiisomorphism.

Two-dimensional vibrational potential energy surface for the ring bending and twisting of 1,3-oxathiolane. Evidence for the anomeric effect resulting from –O–CH2–S– linkages

The far-infrared spectra of 1,3-oxathiolane and its 2,2-d2 isotopomer have been analyzed in terms of a two-dimensional vibrational potential energy surface expressed as a function of ring-bending and ring-twisting coordinates. The barrier to planarity was determined to be 2289±200 cm−1 while the barrier to pseudorotation, representing the energy difference between the lowest energy twisted form and the highest energy bent form, was found to be 570±20 cm−1. The barrier to planarity is about 500 cm−1 higher than that of cyclopentane, and this is attributed to the anomeric effect resulting from the –O–CH2–S– linkage which tends to twist the molecule out of the planar configuration.

(4,7-Dimethyl-4,7-diazadecanediamide)diisothiocyanatocopper(II)

The Cu II of the title complex, [Cu(NCS) 2 (C 10 H 22 O 2 N 4 )], is six-coordinated in a tetragonally elongated octahedral geometry with the two amine N atoms of the quadridendate ligand and the two N atoms of the isothiocyanato groups equatorial and the two amide O atoms axial. The two N-methyl groups of the tetradendate ligand are trans to each other with respect to the equatorial plane. The complex has a cis-α conformation. The central five-membered ring is in a stable skew form and both of the terminal six-membered rings are in unstable twist forms

ChemInform Abstract: Electronic Structure and Potential Energy Surfaces of the Ethylene Radical Cation at and in the Vicinity of the 90 °‐Twisted Form.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Conformation of Methyl trans-3-Arylpropenoates in Triplet States and Their Reactivities

Abstract The photochemical cis–trans isomerization and cycloaddition of methyl trans-3-arylpropenoates in benzene via triplet state were investigated. The results of triplet sensitized cis–trans isomerization clearly indicated that the most stable conformation for methyl 3-phenylpropenoate is a twisted form while methyl 3-(4-biphenylyl)propenoate and methyl 3-(2-naphthyl)propenoate are in the equilibrium states between the trans-planar triplet and twisted form. Photoirradiation of these methyl 3-arylpropenoates in relatively high concentrated benzene solutions gave two isomeric cyclodimers of dimethyl t-3, t-4-diaryl-r-1, c-2-cyclobutanedicarboxylate and dimethyl c-3, t-4-diaryl-r-1, t-2-cyclobutanedicarboxylate as main products. The reactivities of cycloaddition are relatively high where the most stable conformation is twisted form.

Electronic structure and potential energy surfaces of the ethylene radical cation at and in the vicinity of the 90°-twisted form

The potential energy surfaces of the ethylene radical cation near the 90°-twisted form were clarified by an appropriate configuration interaction calculation. A characteristic conical intersection between the ground doublet and the first excited doublet states at a D2d 90°-twisted geometry was revealed. It was found that spin-charge separation occurs suddenly near the twist angle of 90°. The effect of substitution on the shape of the potential energy surfaces is also discussed.

Molecular and crystal structure of 1?1 guest-host bis(hexafluoroacetylacetonato)calcium complex with 18-crown-6

We have carried out an X-ray structural study of the title complex (a CAD-4F diffractometer, λMoKα, graphite monochromator, ω/2Θ scan mode, θmax, direct methods, 1465 reflections, R=0.036). Crystals are monoclinic with a=17.971(13), b=13.475(3), c=13.379(8) A, β=106.67(5)°, Z=4CaO10C22H26F12, space group C2/c, d calc =1.537 g/cm3. The complex (C2 symmetry) has a molecular structure and belongs to the guest-host type. The Ca atom is located in the center of the 18-crown-6 cavity; bidentate hexafluoroacetylacetonate guest ligands occupy the trans-positions relative to the plane of a maxidentate macrocycle. The Ca−O distances in a ten-vertex Ca polyhedron are 2.474–2.666 A. The macrocycle conformation is characterized by six gauche C−C bonds and two gauche and ten trans C−O bonds. The dihedral COCC angle differs significantly (by 38.1°) from the angle of 60°, which is common to a gauche conformation. The six-membered cycle formed by oxygen atoms has a twist form with the annular O−O distances of 5.132–5.329 A. Structural features explaining an easy sublimation of the compound are discussed.

Designed molecules reproducing the two conformations of teleocidins.

Tumor-promoting teleocidins are known to exist in an equilibrium between two conformational states, the twist form and sofa form, in solution. Benzolactam-Vs, in which the indole ring of indolactams was replaced with a benzene ring, were designed in an attempt to reproduce the active conformation of teleocidins, and synthesized. The 8-membered lactam (benzolactam-V8-310) exists only in the twist form in solution and the 9-membered lactam (benzolactam-V9-310) exists only in the sofa form in solution. The stronger biological activities of the 8-membered lactam than those of indolactam-V and the lack of activity of the 9-membered lactam clearly indicated that active conformation for tumor-promoting activity of teleocidins is close to the twist form.

New genera of Upper Ordovician triplesiid brachiopods from Sweden

Abstract Three new genera of triplesiid brachiopods are proposed. Ogmoplecia is a widespread Ashgill form that includes coarse ribbed species hitherto placed in Oxoplecia but characterised by a grooved cardinal process and a predominantly smooth pseudodeltidium lacking the median fold (monticulus) typical of the superfamily. Details of the mantle canal system are recorded from silicified internal moulds of the type material from Oland. Grammoplecia, in essence a capillate Triplesia, is again fairly widely distributed, in the Ashgill and Caradoc, possibly occurring as early as the Llandeilo; the capillae display characteristics atypical of standard radial ornamentation. Amphiplecia is a twisted form with a sinusoidal anterior commissure, abundant in the Ashgill Boda Limestone of central Sweden but otherwise so far known only from occasional specimens in the Caradoc and Ashgill of Ringerike, Oslo Region, Norway.

The algebraic K-theory of the classical groups and some twisted forms

The algebraic K-theory of the classical groups and some twisted forms

Polymerization of coordinated monomers. XXII. Ab initio molecular orbital study on the binary radical complexes of 2‐methoxycarbonyl propyl radical with boron trichloride and with boron trifluoride as a model of growing radical end

AbstractThe geometrical and electronic structures of the binary radical complexes of 2‐methoxycarbonyl propyl radical with boron trichloride and with boron trifluoride were determined by using an ab initio molecular orbital method. The 2‐methoxycarbonyl propyl radical complex was a model of the growing radical end in the copolymerization of methyl methacrylate in the presence of boron halides. The most stable structure of the binary radical complex composed of 2‐methoxycarbonyl propyl radical with boron trichloride was a twisted form in which the dihedral angle between the vinyl group and the ester group was 32°, while that of the binary radical complex composed of methyl methacrylate radical with boron trifluoride was a planar form as the free radical. The frontier orbital energy of 2‐methoxycarbonyl propyl radical was lowered by 0.06 au by the coordination of boron trichloride, while that was lowered only by 0.02 au by the coordination of boron trifluoride. The polymerization mechanism was elucidated on the basis of these predictions. © 1993 John Wiley &amp; Sons, Inc.

Time resolved fluorescence and solvatochromism in donor-substituted bianthrones

The influence of donor substitution of the bianthrone system is investigated through the solvatochromism of the absorption and fluorescence spectra as well as time resolved fluorescence measurements. Both the absorption and fluorescence spectra show a strong solvatochromic shift indicative of an increased dipole moment in the excited state resulting from a charge transfer from the donor to the ring system. The fluorescence lifetime and yield are also seen to be strongly solvent dependent, both decreasing with increasing polarity which is indicative of the increased favouring of nonradiative routes with increasing polarity. A strong dependence of the lifetime on temperature in a glassy solvent mixture leads to the assignment of this nonradiative channel to the twisted form of the bianthrone moiety which is stabilised by the charge transfer process.

Time resolved fluorescence and solvatochromism in donor-substituted bianthrones

The influence of donor substitution of the bianthrone system is investigated through the solvatochromism of the absorption and fluorescence spectra as well as time resolved fluorescence measurements. Both the absorption and fluorescence spectra show a strong solvatochromic shift indicative of an increased dipole moment in the excited state resulting from a charge transfer from the donor to the ring system. The fluorescence lifetime and yield are also seen to be strongly solvent dependent, both decreasing with increasing polarity which is indicative of the increased favouring of nonradiative routes with increasing polarity. A strong dependence of the lifetime on temperature in a glassy solvent mixture leads to the assignment of this nonradiative channel to the twisted form of the bianthrone moiety which is stabilised by the charge transfer process.