Arbitrary Twists Research Articles

Franz Rosenzweig’s Account of Revelation in Light of Its Protestant Background

AbstractIn the subsection “Grammar of Eros (The Language of Love)” in section 2 of book 2 of The Star of Redemption, the beating heart of the work, Franz Rosenzweig offers a peculiar portrait of the event of revelation. What is presented is a dramatization of the encounter between the loving God and the beloved human soul, a developing scene consisting of a series of utterances and experiences, many of which appear unwarranted. Why does Rosenzweig present revelation in this manner? This article seeks to explain the seemingly arbitrary twists and turns in the dramatized “plot” through which Rosenzweig depicts revelation by demonstrating that it follows in its main features the prevalent Protestant understanding of revelation as encompassing not only divine self-disclosure but also the discovery of sin, confession, forgiveness of sin, reconciliation, attainment of selfhood, and redemption, and is framed according to the directives of the Lutheran foundational principle of “at once a sinner and justified (Simul Justus et Peccator). In so doing, it exhibits Rosenzweig’s deep embeddedness in the Protestant theological discourse of his time and shows that The Star should be understood in light of the contemporary Protestant theology.

Hofer–Zehnder capacity of disc tangent bundles of projective spaces

AbstractWe compute the Hofer–Zehnder capacity of disc tangent bundles of the complex and real projective spaces of any dimension. The disc bundle is taken with respect to the Fubini–Study resp. round metric, but we can obtain explicit bounds for any other metric. In the case of the complex projective space, we also compute the Hofer–Zehnder capacity for the magnetically twisted case, where the twist is proportional to the Fubini–Study form. For arbitrary twists, we can still give explicit upper bounds.

Form-factors and complete basis of observables via separation of variables for higher rank spin chains

Integrable mathfrak{sl} (N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of Variables (FSoV) technique with a new tool called Character Projection to compute all matrix elements of a complete set of operators, which we call principal operators, in the basis diagonalising the tower of conserved charges as determinants in Q-functions. Building up on these results we then derive similar determinant forms for the form-factors of combinations of multiple principal operators between arbitrary factorizable states, which include, in particular, off-shell Bethe vectors and Bethe vectors with arbitrary twists. We prove that the set of principal operators generates the complete spin chain Yangian. Furthermore, we derive the representation of these operators in the SoV bases allowing one to compute correlation functions with an arbitrary number of principal operators. Finally, we show that the available combinations of multiple insertions includes Sklyanin’s SoV B operator. As a result, we are able to derive the B operator for mathfrak{sl} (N) spin chains using a minimal set of ingredients, namely the FSoV method and the structure of the SoV basis.

Possible high temperature superconducting transitions in disordered graphite obtained from room temperature deintercalated KC[formula omitted

Although progress with twisted graphene nano-devices is boosting the superconductivity that is the consequence of their Moiré flat electronic bands, the immense choice for future development is an obstacle for their optimisation. We report here that soft-chemistry deintercalation of KC8 breaks down graphite stacking generating a strong disorder that includes stacking twists and variable local doping. We obtain a bulk graphite whose individual crystallites have different stackings with arbitrary twists and doping, scanning in the same sample a huge number of stacking configurations. We perform magnetisation measurements on batches with different synthesis conditions. The disorder weakens the huge diamagnetism of graphite, revealing several phase transitions. A tiny “ferromagnetic-like” magnetisation appears with Curie temperatures T0∼ 450 K, that has to be subtracted from the measured magnetisation. Depending on sample synthesis, anomalies towards diamagnetic states appear at Tc∼ 110 K (3 samples), ∼ 240 K (4 samples), ∼ 320 K (2 samples). Electrical resistivity measurements yield anomalies for the Tc∼ 240 K transition, with one sample showing a 90% drop. We discuss the possibility that these (diamagnetic and resistive) anomalies could be due to superconductivity. As the amount of these phases is small by construction, fine-tuning of the process will be necessary to increase their fraction and select the desired phase.

Wide moments of L-functions II: dirichlet L-functions

Abstract We study wide moments of Dirichlet L-functions using analytic properties of the Lerch zeta function. Among other things we obtain an asymptotic expansion of wide moments of Dirichlet L-functions (with arbitrary twists) extending results of Heath-Brown. We also give applications to non-vanishing.

Equivariant higher twisted K$K$‐theory of SU(n)$SU(n)$ for exponential functor twists

We prove that each exponential functor on the category of finite-dimensional complex inner product spaces and isomorphisms gives rise to an equivariant higher (that is, non-classical) twist of K $K$ -theory over G = S U ( n ) $G=SU(n)$ . This twist is represented by a Fell bundle E → G $\mathcal {E}\rightarrow \mathcal {G}$ , which reduces to the basic gerbe for the top exterior power functor. The groupoid G $\mathcal {G}$ comes equipped with a G $G$ -action and an augmentation map G → G $\mathcal {G}\rightarrow G$ , that is an equivariant equivalence. The C ∗ $C^*$ -algebra C ∗ ( E ) $C^*(\mathcal {E})$ associated to E $\mathcal {E}$ is stably isomorphic to the section algebra of a locally trivial bundle with stabilised strongly self-absorbing fibres. Using a version of the Mayer–Vietoris spectral sequence, we compute the equivariant higher twisted K $K$ -groups K ∗ G ( C ∗ ( E ) ) $K^G_*(C^*(\mathcal {E}))$ for arbitrary exponential functor twists over S U ( 2 ) $SU(2)$ , and also over S U ( 3 ) $SU(3)$ after rationalisation.

Twisted circle compactifications of 6d SCFTs

We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data.

Electronic structure theory of weakly interacting bilayers

We derive electronic structure models for weakly interacting bilayers such as graphene-graphene and graphene-hexagonal boron nitride, based on density functional theory calculations followed by Wannier transformation of electronic states. These transferable interlayer coupling models can be applied to investigate the physics of bilayers with arbitrary translations and twists. The functional form, in addition to the dependence on the distance, includes the angular dependence that results from higher angular momentum components in the Wannier $p_z$ orbitals. We demonstrate the capabilities of the method by applying it to a rotated graphene bilayer, which produces the analytically predicted renormalization of the Fermi velocity, van Hove singularities in the density of states, and Moir\'{e} pattern of the electronic localization at small twist angles. We further extend the theory to obtain the effective couplings by integrating out neighboring layers. This approach is instrumental for the design of van der Walls heterostructures with desirable electronic features and transport properties and for the derivation of low-energy theories for graphene stacks, including proximity effects from other layers.

Stable averages of central values of Rankin–Selberg L -functions: Some new variants

As shown by Michel and Ramakrishnan (2007) and later generalized by Feigon and Whitehouse (2008), there are “stable” formulas for the average central L -value of the Rankin–Selberg convolutions of some holomorphic forms of fixed even weight and large level against a fixed imaginary quadratic theta series. We obtain exact finite formulas for twisted first moments of Rankin–Selberg L -values in much greater generality and prove analogous “stable” formulas when one considers either arbitrary modular twists of large prime power level or real dihedral twists of odd type associated to a Hecke character of mixed signature.

Digital Media, 419, and the Politics of the Global Network

In his article Digital Media, 419, and the Politics of the Global Network Paul Benzon analyzes advance fee fraud, a scam in which con artists communicate with potential victims via email, promising them a monetary reward in return for financial assistance in extracting an allegedly astronomical (yet ultimately nonexistent) fortune from within a geographical zone often characterized as highly violent and unstable. Advance fee fraud is often referred to simply as 419, in accordance with the section of Nigerian penal code that addresses fraud. Benzon reads advance fee fraud as a practice of epistolary narrative that self-consciously allegorizes central processes of global financial circulation, trading in digitized narrative information rather than in digitized capital. In this sense, he suggests, it functions as a highly abstract financial instrument within the network of the global economy, dealing in a paradoxically literal fashion with imaginary money and thus using narrative form to probe and problematize the question of how and where money might move as data. Tracing the geopolitical and geoeconomic dimensions of advance fee fraud’s narrative and formal structure, Benzon argues that its random interpellations, arbitrary twists, and exaggerated claims deploy literary narrative in a manner that both relies upon and mirrors the material instability of global digital mediation itself. Paul Benzon, Digital Media, 419, and the Politics of the Global Network page 2 of 10 CLCWeb: Comparative Literature and Culture 13.3 (2011): Thematic issue New Perspectives on Material Culture and Intermedial Practice. Ed. Steven Totosy de Zepetnek, Asuncion Lopez-Varela, Haun Saussy, and Jan Mieszkowski

Twisted Dickson–Mui invariants and the Steinberg module multiplicity

AbstractWe determine the invariants, with arbitrary determinant twists, of the parabolic subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra S•(V) and the exterior algebra ∧•(V) of the natural GLn(q)-module V. In addition, we obtain the graded multiplicity of the Steinberg module of GLn(q) in S•(V) ⊗ ∧•(V), twisted by an arbitrary determinant power.

Twists and Gromov hyperbolicity of riemann surfaces

The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces (with their Poincare metrics). We prove that quasiconformal maps between Riemann surfaces preserve hyperbolicity; however, we also show that arbitrary twists along simple closed geodesics do not preserve it, in general.

Mixed integrable [formula omitted] vertex model with arbitrary twists

We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU ( N ) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete representations of the group SU ( 2 ) and the non-compact group SU ( 1 , 1 ) as well as the conjugate representation of the SU ( N ) symmetry. Introducing certain transformations on the quantum spaces we are able to solve generalized impurity problems including those related to singular matrices.

Twisting warped supergravity

We study gauged five-dimensional supergravity on the interval [0,\pi R]. We find a set of boundary conditions with respect to which the theory is locally supersymmetric. For theories with detuned brane tensions (\Lambda_4<0), we show that these boundary conditions can be used to spontaneously break global supersymmetry. For the original, tuned Randall-Sundrum scenario (\Lambda_4=0), we prove that the locally supersymmetric boundary conditions are also globally supersymmetric. We lift the theory from [0,\pi R] to S^1 and R, with arbitrary twists for the fermions, and cast these results in the language of the Scherk-Schwarz mechanism.

On the non-vanishing of cubic twists of automorphic $L$-series

Let f be a normalised new form of weight 2 for ro(N) over Q and F, its base change lift to Q(v'/=). A sufficient condition is given for the nonvanishing at the center of the critical strip of infinitely many cubic twists of the L-function of F. There is an algorithm to check the condition for any given form. The new form of level 11 is used to illustrate our method. 0. INTRODUCTION There has been a tremendous amount of recent research on the nonvanishing of L-functions. On GL(2), the first results are due to Shimura [15], who proved that a given L-function can be twisted by a character of finite order so that the twisted L-function does not vanish at a certain point. Shimura's nonvanishing results were generalized by Rohrlich [14]. The study of the nonvanishing of quadratic twists rather than arbitrary finite order twists was started by Goldfeld, Hoffstein and Patterson [7] for the CM case, and in greater generality by Waldspurger [16]. This was later complemented by the work of Bump, Friedberg and Hoffstein [2], [3], [5] using metaplectic Eisenstein series and the Rankin-Selberg method. Alternately, analytic number theoretic methods have been used by Murty and Murty [12] and by Iwaniec [10] to obtain nonvanishing results. The first results on the non-vanishing of cubic twists were obtained by Lieman [11]. He applied the theory of automorphic forms on the cubic cover of GL(3) to the L-series of the CM elliptic curve x3+y3 = 1. In this way he obtained a non-vanishing result for cubic twists of the L-series of the automorphic form corresponding to the curve. However, because the curve has complex multiplication, the L-series in this instance is a GL(1) Hecke L-series with grossencharacter. It is this particular fact which made the GL(3) theory applicable. In this paper we will give the first non-vanishing results for cubic twists of autmorphic L-series on GL(2) that are not lifts from GL(1). In particular, we will show that if f is the new form of weight 2 and level 11, then infinitely many cubic twists of the L-series of f are non-zero at the center of the critical strip. It then follows as an immediate corollary that there are infinitely many cubic extensions K of Q(VZ/=W) such that the analytic rank of E = Xo(11) over K is zero. Our approach gives a method of obtaining a similar result for any given GL(2) automorphic form. However, for reasons that will be described below, there is one step in the computation which can be verified for any given form, but which cannot yet be done in general. Received by the editors September 27, 1996 and, in revised form, February 14, 1997. 1991 Mathematics Subject Classification. Primary 11F66; Secondary 11F70, 11M41, 11N75. (D1999 American Mathematical Society 1075 This content downloaded from 157.55.39.145 on Sat, 02 Jul 2016 05:14:40 UTC All use subject to http://about.jstor.org/terms

General Yukawa couplings of strings on [formula omitted] orbifolds

We calculate the four-point correlation of strings on Z N orbifolds, where two strings are allowed to have arbitrary twists, while the others have corresponding anti-twists. This is then factorized in three-point correlations, giving the exact tree-level Yukawa couplings for strings with arbitrary twists.

4d fermionic superstrings with arbitrary twists

We present the rules for systematically constructing all consistent four-dimensional string theories, using free world-sheet fermions which pick up arbitrary phases when parallel transported around the string. These rules are necessary and sufficient for multi-loop modular invariance. They lead to theories with general Z N (GSO-type) projections, whose merits for model-building we discuss. We classify all boundary conditions yielding massless space-time spinors. We show that, in contrast to the case of only real 2d fermions, all possible realizations of world-sheet supersymmetry are now allowed. This opens the way for the construction of a new class of supersymmetric string models.

Analysis and design of multiple-beam appliances

A new approach for the analysis of multiple-beam structures, such as headgear bows, is developed for beams which contain arbitrary curvatures, twists, and material properties. The generalized transfer matrix of a single-beam analysis is converted to a stiffness matrix and inserted into a global matrix which describes the entire system. The effect of inner bow wire size (0.044 inch and 0.051 inch) on the force system is demonstrated. The inner bow with the larger cross section shows only a slight (not clinically significant) reduction in rotational moment and buccal force applied because of its greater ability to resist deformation during the loading process. Small amounts of tooth and/or tube rotations ("play") result in a significant reduction of the crown rotational moment. With increasing rotation of the tube to the inner bow, the high lateral forces and large moments found about the long axis of the teeth are found to reduce. Symmetrical headgears are chosen to illustrate the analysis and to indicate the manner in which this approach may be used to study and design similar orthodontic appliances.