Twisted Form Research Articles

One-loop double copy relation from twisted (co)homology

We propose a geometric relation between closed and open string amplitudes at one-loop. After imposing a homological splitting on the world-sheet torus, twisted intersection theory is used to establish a one-loop double copy relation. The latter expresses a closed string amplitude by a pair of open string amplitudes and twisted intersection numbers. These inner products on the vector space of twisted differential forms are related to the twisted homology and cohomology groups associated with the Riemann-Wirtinger integral.

Flux quantization on M5-branes

We highlight the need for global completion of the field content in the M5-brane sigma-model analogous to Dirac’s charge/flux quantization, and we point out that the superspace Bianchi identities on the worldvolume and on its ambient supergravity background constrain the M5’s flux-quantization law to be in a non-abelian cohomology theory rationally equivalent to a twisted form of co-Homotopy. In order to clearly bring out this subtle point we give a streamlined re-derivation of the worldvolume 3-flux via M5 “super-embeddings”. Finally, assuming the flux-quantization law to actually be in co-Homotopy (“Hypothesis H”) we show how this implies Skyrmion-like solitons on general M5-worldvolumes and (abelian) anyonic solitons on the boundaries of “open M5-branes” in heterotic M-theory.

A spectral theorem for compact representations and non-unitary cusp forms

We show that a compact representation of either a semisimple Lie group or a totally disconnected group has a filtration with irreducible subquotients of finite multiplicity. In the Lie group case we show the stronger assertion, that it has an orthogonal decomposition into summands of finite lengths. This generalises and simplifies a number of more special spectral theorems in Deitmar and Monheim (Math Z 284(3–4):1199–1210, 2016, https://doi.org/10.1007/s00209-016-1695-9), Müller (Int Math Res Not 9(2):2068–2109, 2011), Venkov (in: Proceedings of the Steklov Institute of Mathematics, no. 4(153), ix+163 pp. (1983), 1982). We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms. We finally show that the space of cusp forms is complemented by the space of Eisenstein series.

An AIE-active Schiff base derivative with reversible thermochromism based on two-step isomerization in the solid state

Thermoresponsive aggregation-induced emission (AIE) luminogens, especially in the solid state, have attracted extensive attention due to their potential applications as smart materials. Herein, we report an AIE-active tetraphenylethene (TPE)-based Schiff base derivative (TPENOMe-I) that exhibits rapid and reversible thermochromism along with luminescence in the solid state. The excited-state intramolecular proton transfer-induced AIE and efficient thermochromism (rather than photochromism) are facilitated by the relatively compact crystal packing and polymorphism of TPENOMe-I, which effectively suppress cis-to-trans isomerization. Theoretical calculations demonstrated that the two-step isomerization process between the enol isomer and the cis- and twisted cis-keto isomers is responsible for the thermochromic behavior of solid-state TPENOMe-I. The chromic transitions may result from the reversible interconversion between various twisted cis-keto forms during the thermal isomerization process. Three composites containing TPENOMe-I that were simply prepared with low cost excited reversible thermochromism and were successfully demonstrated in thermochromic patterns. The findings suggest that these TPENOMe-I composites have promising applications for use in warning labels, thermochromic textiles, and thermal printing.

Mass concentration of plastic particles from two-dimensional images

Imaging techniques play a crucial role in characterizing environmental plastics. However, most reported findings rely on two-dimensional projections of particles resting on flat surfaces. This limitation makes it challenging to accurately determine mass concentration, which is essential for deriving toxicologically relevant exposure data. The primary issue arises from the loss of information regarding particle height or thickness. This study aims to evaluate the assumptions necessary to compensate this loss of information. To achieve this, we used a set of environmental plastic particles, mesoplastics and microplastics, from marine campaigns, and precisely measured their three spatial dimensions and mass. Our study demonstrated the feasibility of estimating the mass of plastic particles through two-dimensional images. However, for enhanced accuracy, additional information derived from the dataset of particles under examination is necessary. Specifically, estimating the mass of platelike particles requires information about their height. Similarly, calculating the volume for elongated shapes as cylinders, should be limited to particles with the same width and height and for which their length can be precisely determined, even if the image depicts twisted forms. In conclusion, while obtaining mass concentration from single two-dimensional images enables reasonable estimations, achieving the precision needed for exposure data requires acquiring additional information from the sample and carefully considering the shape of each individual particle.

Tunable Nano-Bending Structures of Loosened/Tightened Lassos with Bi-Stable Vibration-Induced Emissions for Multi-Manipulations of White-Light Emissions and Sensor Applications.

The first tunable nano-bending structures of [1]rotaxane containing a single-fluorophoric N,N'-diphenyl-dihydrodibenzo[a,c]phenazine (DPAC) moiety (i.e., [1]RA) are developed as a loosened lasso structure to feature the bright white-light emission [CIE (0.27, 0.33), Φ = 21.2%] in THF solution, where bi-stable states of bending and twisted structures of DPAC unit in [1]RA produce cyan and orange emissions at 480 and 600nm, respectively. With acid/base controls, tunable loosened/tightened nano-loops of corresponding [1]rotaxanes (i.e., [1]RA/[1]RB) can be achieved via the shuttling of macrocycles reversibly, and thus to adjust their respective white-light/cyan emissions, where the cyan emission of [1]RB is obtained due to the largest conformational constraint of DPAC moiety in its bending form of [1]RB with a tightened lasso structure. Additionally, the non-interlocked analog M-Boc only shows the orange emission, revealing the twisted form of DPAC fluorophore in M-Boc without any conformational constraint. Moreover, the utilization of solvents (with different viscosities and polarities), temperatures, and water fractions could serve as effective tools to adjust the bi-stable vibration-induced emission (VIE) colors of [1]rotaxanes. Finally, tuning ratiometric emission colors of adaptive conformations of DPAC moieties by altering nano-bending structures in [1]rotaxanes and external stimuli can be further developed as intelligent temperature and viscosity sensor materials.

Sign involutions on para-abelian varieties

We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil–Châtelet group is annihilated by two. If these equivalent conditions hold, we prove that the Picard scheme of the quotient is étale and contains no points of finite order. In dimension one, such quotients are Brauer–Severi curves, and we analyze the ensuing embeddings of the genus-one curve into twisted forms of Hirzebruch surfaces and weighted projective spaces.

Twisted Blanchfield pairings and twisted signatures III: Applications

Abstract This paper describes how to compute algorithmically certain twisted signature invariants of a knot $K$ using twisted Blanchfield forms. An illustration of the algorithm is implemented on $(2,q)$ -torus knots. Additionally, using satellite formulas for these invariants, we also show how to obstruct the sliceness of certain iterated torus knots.

Quadratic twist of an elliptic curve in a generalized Weierstrass equation over a function field

This paper mainly focuses on the construction of a quadratic twist for an elliptic curve represented in a generalized Weierstrass equation over the field Fq(t). The specific form of the quadratic twist, presented in the generalized Weierstrass equation, is determined by linear algebra approach and discussed in detail.

Exploring twist-4 chiral-even GPDs in the light-front quark-diquark model

In this work, we delve into the realm of quantum chromodynamics (QCD) by calculating twist-4 chiral-even generalized parton distributions (GPDs), within the context of the light-front quark-diquark model (LFQDM), focusing specifically on the intriguing case of zero skewness. To shed light on the behavior of twist-4 chiral-even GPDs, we present comprehensive two-dimensional (2-D) and 3-dimensional (3-D) plots, mapping their dependence on the longitudinal momentum fraction (x) and the momentum transfer (t). Furthermore, our research looks into the profound connection between twist-4 chiral-even GPDs and other distribution functions (DFs), including parton distribution functions (PDFs), transverse momentum-dependent parton distributions (TMDs) and generalized transverse-momentum dependent parton distributions (GTMDs). Additionally, our investigation extends to the exploration of related higher twist form factors (FFs), which play a pivotal role in elucidating the internal structure of hadrons. To provide significant insights into the partons spatial distribution, we have also yielded impact parameter GPD plots.

A novel fiber‐reinforced polymer rope: Simulation and theoretical investigation

AbstractThe study proposed using twisted rope made of flexible fiber‐reinforced polymers (FRPs) instead of wire and synthetic ropes in high load‐bearing and corrosive environments. Finite element model verification and parameter analysis were conducted for the rope, along with deriving theoretical equations for its tensile properties. Increasing the lay length improved model accuracy, with a maximum bearing capacity within a 10% margin of error compared to experimental results. The model length had minimal impact on calculation results, while changes in radial mesh size (0.13 and 0.2 mm) and friction coefficient (0–0.2) greatly affected maximum contact stress. The tensile strength and elastic modulus of the strand remained almost constant (approximately 1142 MPa and 44 GPa) when the friction coefficient was altered. Increasing lay length (6D–20D) enhanced the tensile properties of the strand, whereas tendon diameter (1–3 mm) had negligible impact. Arranging inner and outer strands with the same lay length was better for circular ropes than those with the same lay angle. Inverse lay direction reduced rope torque and increased strand contact stress. Rectangular ropes had higher strength and modulus conversion efficiency, with lower contact stress compared to circular ones. The accuracy of rope equations improved with longer lay lengths, and adding a correction factor for lay length can modify the equation.Highlights A flexible FRP rope with high strength and twisted form was proposed. The effect of construction factors on the tensile behaviors of ropes was clarified. Equations for calculating the tensile properties of ropes were derived.

Generalizations of quasielliptic curves

We generalize the notion of quasielliptic curves, which have infinitesimal symmetries and exist only in characteristic two and three, to a remarkable hierarchy of regular curves having infinitesimal symmetries, defined in all characteristics and having higher genera. This relies on the study of certain infinitesimal group schemes acting on the affine line and certain compactifications. The group schemes are defined in terms of invertible additive polynomials over rings with nilpotent elements, and the compactification is constructed with the theory of numerical semigroups. The existence of regular twisted forms relies on Brion's recent theory of equivariant normalization. Furthermore, extending results of Serre from the realm of group cohomology, we describe non-abelian cohomology for semidirect products, to compute in special cases the collection of all twisted forms.

Effective Encapsulation and Surface Treatment for Damp‐Heat Stable Triple Cation Perovskite Solar Cells

Multiple‐cation perovskites have been extensively researched for stability enhancement, but limited literature exists on CsFAMA (CFM) solar cell stability under harsh temperature and humidity. This article focuses on the development of damp‐heat‐resistant CFM‐based perovskite solar cells (PSCs) through the implementation of various surface treatment strategies, including antisolvent treatment (AST) control and alkyl‐type interfacial passivation, while also proposing an effective encapsulation structure. The Cs+ ratio in Csx(FA0.91MA0.09)1−xPb(I,Br)3 perovskites is varied in the range of x = 0 to 0.362, and the AST times are explored by adjusting from 8 to 15 s. Remarkably, a power conversion efficiency (PCE) is achieved with significant improvements in open‐circuit voltage and fill factor at an AST time of 12 s. Through precise tuning of the Cs ratio to x = 0.17 (Cs0.17(FA0.91MA0.09)0.83Pb(I,Br)3) and introduction of an octyl‐ammonium iodide interlayer, the highest‐performing device with a PCE of 20.82% is obtained. Additionally, a low‐temperature vacuum lamination is employed, and the conducive tape in a twisted form is extended, which effectively seals the device. This results in superior stability for 500 h under damp‐heat conditions at 85 °C and 85% relative humidity. This encapsulation method holds significant promise as a potential solution for the modularization of PSCs.

Prevalence and factors associated with domestic violence amongst married women in urban and rural areas of Kano State, Nigeria

Domestic violence against women, in its various forms, remains endemic in communities and countries globally and is coupled with contributing marital disharmonies, adverse health outcomes on the victims, their children, immediate families and the community. The study assessed and compared prevalence and factors associated with DV amongst married women in urban and rural areas of Kano, Nigeria. Using a comparative cross-sectional study design, 493 married women were studied. Multistage sampling technique was used to select respondents and data collected using an adapted structured interviewer administered questionnaire. Analysis was done using SPSS vs 25. The overall prevalence of DV was 23%; of which less than a quarter of the urban (17%) and over three quarters of the rural (83%) married women experienced at least one form of DV. Most reported forms in the urban vs rural were: verbal abuse (in form of humiliation, insults and threatening to attack) 15% vs 83%; physical abuse (in form of push, slap, and arm twisting) 6% vs 28%. Older age (women > 45 years) [p=0.00, AOR=0.228, 95% CI=0.096-0.539], and husband’s non-smoking habit [p=0.00, AOR=0.226, 95% CI=0.110-0.467] were protective for the experience of domestic violence. DV was prevalent among married women particularly among those living in the rural area and the younger women. Women whose husbands engaged in smoking were more at risk. Efforts should be made to provide education and support for vulnerable women exposed to DV.

Fiberwise criteria for twisted forms of algebraic structures

We provide a criterion for certain algebraic objects over Jacobson schemes to be forms of each other based on their behaviour at closed fibres. This criterion permits to answer a question related to current and affine Kac-Moody Lie algebras that I. Burban had asked the authors.

Flexural-torsional analysis of steel beam structures using ANSYS

The theories for uniform torsion and non-uniform torsion are studied. The aim of the paper is to study the behaviour of the beams of different sections for combined bending and torsion under various loadings and support conditions. The comparative study of the finite element for beams with different geometry sections of solid and hollow circular sections, rectangular section and symmetric I sections subjected to concentric and eccentric loading conditions with simply supported and cantilever end conditions is presented using ANSYS 18.1 workbench. The length of the beam is kept constant as 4 m. The transverse and axial deformation, the equivalent stresses and strains of beams were studied along with the mode of failure and effect of bending and torsion. It was observed that concentric loading resulted in transverse deflections while the torsional moment loading causes in-plane deformation in form of twisting of the cross-section with maximum stress generation and the eccentric loading results in combined transverse and in-plane axial deformation. From the result obtained it can be said that open sections has lesser efficiency for torsional and eccentric type loading as higher stresses and axial deflections were observed as compared to the hollow circular and rectangular sections.

Conformational Relaxation Dynamics of Poly(3-hexylthiophene) Photoexcited in Solution as Studied by Femtosecond Time-Resolved Stimulated Raman Spectroscopy in 1190-1550 nm Region.

When a conjugated polymer is photoexcited in solution, its effective conjugation length in the singlet exciton state often increases through the conformational relaxation of the polymer main chain and/or hopping of the excitation. We measured femtosecond time-resolved near-IR stimulated Raman spectra of poly(3-hexylthiophene) (P3HT) photoexcited in four organic solvents for understanding the dynamics of the exciton elongation through the conformational relaxation separately from that through the exciton hopping. In the ring CC stretch frequency region, a band appears at around 1415 cm-1 and decays, while a new band rises at around 1370 cm-1. The average time constant of the change is estimated to be 8.7-19 ps and correlated almost linearly with the viscosity of the solvents. These results suggest that the main chain of P3HT in the singlet exciton state relaxes from a twisted form to a planar form in the 0-100 ps range when it surmounts an activation barrier of 5.8-7.8 kJ mol-1, generated possibly by the steric effect of the hexyl side group. When the rise of the 1370 cm-1 band is analyzed in detail, it is reproduced with two exponential rise functions with time constants of 0-3.3 and 16-22 ps. The two rise components suggest that a portion of P3HT forms a cluster in solution, while the other portion of P3HT is isolated.

Intersections of twisted forms: New theories and double copies

Tree–level scattering amplitudes of particles have a geometrical description in terms of intersection numbers of pairs of twisted differential forms on the moduli space of Riemann spheres with punctures. We customize a catalog of twisted differential forms containing both already known and new differential forms. By pairing elements from this list intersection numbers of various theories can be furnished to compute their scattering amplitudes. Some of the latter are familiar through their CHY description, but others are unknown. Likewise, certain pairings give rise to various known and novel double–copy constructions of spin–two theories. This way we find double copy constructions for many theories, including higher derivative gravity, (partial massless) bimetric gravity and some more exotic theories. Furthermore, we present a derivation of amplitude relations in intersection theory.

Two 3D Two-Fold Interpenetrated Dia-Like Polyoxometalate-Based Metal-Organic Frameworks: Synthesis and Sulfide Selective Oxidation Activity.

Two new three-dimensional (3D) polyoxometalate-based metal-organic frameworks (POMOFs), [M2(btap)4(H2O)4(HPMo10VI Mo2VO40)] (M = Co (1) and Cd (2); btap = 3, 5-bis(1', 2', 4'-triazol-1'-yl)pyridine), have been synthesized under mild hydrothermal conditions and characterized in detail. Single-crystal X-ray diffraction (SXRD) analysis indicates that 1 and 2 are isostructural. In complexes 1 and 2, the metal ion is coordinated with the ligand to form two different left and right helical one-dimensional chains, which are alternately connected in a twisted form to build a two-fold interpenetrated three-dimensional structure, and the polyoxometalate is encapsulated into in the pores generated by the interpenetrating structure. It is noteworthy that 1 and 2, as recyclable catalysts, possess favorable heterogeneous catalytic activity and excellent sulfoxide selectivity in sulfide oxidation reactions, with H2O2 as an oxidant. By reason of the high dispersion of polyoxometalate with good intrinsic activity in the skeleton structure, the title complex has high activity. In addition, no obvious decrease of sulfoxide yield is observed after at least five cycles. These results indicate the excellent catalytic activity and sustainability of 1 and 2.

Homotopy Double Copy of Noncommutative Gauge Theories

We discuss the double-copy formulation of Moyal–Weyl-type noncommutative gauge theories from the homotopy algebraic perspective of factorisations of L∞-algebras. We define new noncommutative scalar field theories with rigid colour symmetries taking the role of the zeroth copy, where the deformed colour algebra plays the role of a kinematic algebra; some of these theories have a trivial classical limit but exhibit colour–kinematics duality, from which we construct the double copy theory explicitly. We show that noncommutative gauge theories exhibit a twisted form of colour–kinematics duality, which we use to show that their double copies match with the commutative case. We illustrate this explicitly for Chern–Simons theory, and for Yang–Mills theory where we obtain a modified Kawai–Lewellen–Tye relationship whose momentum kernel is linked to a binoncommutative biadjoint scalar theory. We reinterpret rank-one noncommutative gauge theories as double copy theories and discuss how our findings tie in with recent discussions of Moyal–Weyl deformations of self–dual Yang–Mills theory and gravity.