We prove that chaotic flows (i.e. flows that satisfy the shadowing property and have a dense subset of periodic orbits) satisfy a reparametrized gluing orbit property similar to the one introduced in ...Bomfim and Varandas (2015). In particular, these are strongly transitive in balls of uniform radius. We also prove that the shadowing property for a flow and a generic time-t map, and having a dense subset of periodic orbits hold for a C0-Baire generic subset of Lipschitz vector fields, that generate continuous flows. Similar results also hold for C0-generic homeomorphisms and, in particular, we deduce that chain recurrent classes of C0-generic homeomorphisms have the gluing orbit property.
A
bstract
We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant ...massive-spinor formalism, and flesh out some of its details along the way. Thanks to the compact form of the resulting amplitudes, many of their properties, and in particular the constraints of perturbative unitarity, are easily seen in this formalism. Our approach is purely bottom-up, assuming just the standard-model electroweak spectrum as well as the conservation of electric charge and fermion number. The most general massive three-point amplitudes consistent with these symmetries are derived and studied in detail, as the primary building blocks for the construction of scattering amplitudes. We employ a simple argument, based on tree-level unitarity of four-point amplitudes, to identify the three-point amplitudes that are non-renormalizable at tree level. This bottom-up analysis remarkably reproduces many low-energy relations implied by electroweak symmetry through the standard-model Higgs mechanism and beyond it. We then discuss four-point amplitudes. The gluing of three-point amplitudes into four-point amplitudes in the massive spinor helicity formalism is clarified. As an example, we work out the
ψ
c
ψ Zh
amplitude, including also the non-factorizable part. The latter is an all-order expression in the effective-field-theory expansion. Further constraints on the couplings are obtained by requiring perturbative unitarity. In the
ψ
c
ψ Zh
example, one for instance obtains the renormalizable-level relations between vector and fermion masses and gauge and Yukawa couplings. We supplement our bottom-up derivations with a matching of three- and fourpoint amplitude coefficients onto the standard-model effective field theory (SMEFT) in the broken electroweak phase. This establishes the correspondence with the usual Lagrangian approach and paves the way for SMEFT computations in the on-shell formalism.
The steel cord conveyor belt surface is prone to damage in mining. The worn belt surface has acceleration characteristics, so timely and rapid repair is very necessary. To quickly and automatically ...repair the worn belt surface is a core design objective of the gluing robot (GR). Based on this objective, a new variant Traveling Salesman Problem (TSP) is put forward: after the worn segments are divided according to the worn information and GR's workspace, path optimization of the gluing robot (POGR) problem is presented at a certain worn segment; then the POGR is simplified into a "double vertices" TSP problem by Hamilton graph, and the mathematical model is built. An improved genetic algorithm (IGA) is proposed to handle the POGR problem, which is called IGA-POGR. The main benefit of the proposed IGA-POGR is the ability to solve POGR of different scales in different ways. The performance of the IGA-POGR is illustrated on four well-known TSP problems. Numerical results show that IGA-POGR does not give any deviation (0%) from the optimal solution. Compared with discrete particle swarm optimization (DPSO), IGA-POGR has better performance in terms of the solving quality and time consumption when solving four idealized POGR problems.
G1 spline functions for point cloud fitting Marsala, Michelangelo; Mantzaflaris, Angelos; Mourrain, Bernard
Applied mathematics and computation,
01/2024, Letnik:
460
Journal Article
Recenzirano
Odprti dostop
In this work we present a new construction of basis functions that generate the space of geometrically smooth splines on an unstructured quadrilateral mesh. The basis is represented in terms of ...biquintic Bézier polynomials on each quadrilateral face. The gluing along the face boundaries is achieved using quadratic gluing data functions, leading to globally G1–smooth spaces. We analyze the latter space and provide a combinatorial formula for its dimension as well as an explicit basis construction. Moreover, we assess the use of this basis in point cloud fitting problems. To apply G1 least squares fitting, a quadrilateral structure as well as parameters in each quadrilateral is required. Even though the general problem of segmenting and parametrizing point clouds is beyond the focus of the present work, we describe a procedure that produces such a structure as well as patch-local parameters. Our experiments demonstrate the accuracy and smoothness of the obtained reconstructed models in several challenging instances.
•We propose a new construction of G1 smooth basis functions on a quadrangular mesh.•We use quadratic gluing data functions and provide general, closed form solutions to the G1 constraint system returning the coefficients defining the basis functions.•We solved the fitting problem using least square approach in the space spanned by the proposed G1 spline bases defined on the quad mesh.•We show the quality of these basis functions in fitting problems, presenting several numerical experiments.
A
bstract
Some AdS
3
×
M
7
type IIB vacua have been recently proposed to arise from D3-branes wrapped on a spindle, a sphere with conical singularities at the poles. We explicitly construct a ...generalization of these solutions corresponding to a class of electrically charged and rotating supersymmetric black strings in AdS
5
×
S
5
with general magnetic fluxes on the spindle. We then perform a counting of their microstates using the charged Cardy formula. To this purpose, we derive the general form of the anomaly polynomial of the dual
N
= (0
,
2) CFT in two dimensions and we show that it can be obtained via a simple gluing procedure.
Sensitive, specific, yet multifunctional tattoo‐like electronics are ideal wearable systems for “any time, any where” health monitoring because they can virtually become parts of the human skin, ...offering a burdenless “unfeelable” wearing experience. A skin‐like, multifunctional electronic tattoo made entirely from gold using a standing enokitake‐mushroom‐like vertically aligned nanowire membrane in conjunction with a programmable local cracking technology is reported. Unlike previous multifunctional systems, only a single material type is needed for the integrated gold circuits involved in interconnects and multiplexed specific sensors, thereby avoiding the use of complex multimaterials interfaces. This is possiblebecause the programmable local cracking technology allows for the arbitrary fine‐tuning of the properties of elastic gold conductors from strain‐insensitive to highly strain‐sensitive simply by adjusting localized crack size, shape, and orientations—a capability impossible to achieve with previous bulk cracking technology. Furthermore, in‐plane integration of strain/pressure sensors, anisotropic orientation‐specific sensors, strain‐insensitive stretchable interconnects, temperature sensors, glucose sensors, and lactate sensors without the need of soldering or gluing are demonstrated. This strategy opens a new general route for the design of next‐generation wearable electronic tattoos.
A programmable local cracking technology is proposed for the fabrication of an in‐plane multisensing gold tattoo entirely based on a vertically aligned nanowire membrane. This strategy allows arbitrary fine‐tuning of the properties of elastic gold from stretchable conductors to highly sensitive pressure and strain sensors. By using this method, a multifunctional sensing system without the need of soldering or gluing is demonstrated.
This paper is devoted to the mathematical and computer simulation of multi-parameter systems. We show that the method and algorithm can easily be used in nonlinear net simulation of the systems. ...Simulation is based on experimental data and achieved by the variation of one-dimensional spline approximations. A set of variable one-dimensional splines is the result of simulation. Each of the splines is the image of a section of input parameters area. Software realization is based on the single algorithm that is used repeatedly. The method have been used in investigation some technological conditions of laminating fabrics systems. Specifically, we investigated the stability of gluing joints, hardness and bending of various parts of clothes. Also, we got the simulator of constituent elements of the mixture which may be used in label products as a temperature indicator. The examples eventually demonstrate the efficiency of the presented method.
We describe a homotopical version of the relational and gluing models of type theory, and generalize it to inverse diagrams and oplax limits. Our method uses the Reedy homotopy theory on inverse ...diagrams, and relies on the fact that Reedy fibrant diagrams correspond to contexts of a certain shape in type theory. This has two main applications. First, by considering inverse diagrams in Voevodsky's univalent model in simplicial sets, we obtain new models of univalence in a number of (∞, 1)-toposes; this answers a question raised at the Oberwolfach workshop on homotopical type theory. Second, by gluing the syntactic category of univalent type theory along its global sections functor to groupoids, we obtain a partial answer to Voevodsky's homotopy-canonicity conjecture: in 1-truncated type theory with one univalent universe of sets, any closed term of natural number type is homotopic to a numeral.
Basic constructions over C∞-schemes Olarte, Cristian Danilo; Rizzo, Pedro
Journal of geometry and physics,
August 2023, 2023-08-00, Letnik:
190
Journal Article
Recenzirano
Odprti dostop
C∞-Rings are R-algebras equipped with operations ϕf for every f∈C∞(Rn) and every n∈N. Therefore, a C∞-version of algebraic geometry can be developed using C∞-rings instead of ordinary rings and many ...classical constructions can be performed in this context. In particular, C∞-schemes are the C∞ counterpart of classical schemes. Examples of schemes are often obtained by gluing schemes or using fiber products. Another useful way to give examples of schemes is looking for representable functors F:Schemes→Sets. In this work, we show that constructions such as gluing schemes and fiber products can be done in the context of C∞-algebraic geometry and they can be used to exhibit some examples of C∞-schemes such as projective spaces and Grassmannians as well as necessary and sufficient conditions for a functor F:C∞−Schemes→Sets to be representable.
Paper has been utilized as an ideal platform for chemical, biological, and mechanical sensing for its fibrous structures and properties in addition to its low cost. However, current studies on ...pressure‐sensitive papers have not fully utilized the unique advantages of papers, such as printability, cuttability, and foldability. Moreover, the existing resistive, capacitive, and triboelectric sensing modalities have long‐standing challenges in sensitivity, noise‐proofing, response time, linearity, etc. Here, a novel flexible iontronic sensing mechanism, referred to as iontronic sensing paper (ISP), is introduced to the classic paper substrates by incorporating both ionic and conductive patterns into an all‐in‐one flexible sensing platform. The ISP can then be structured into 2D or 3D tactile‐sensitive origamis only by the paper‐specific manipulations of printing, cutting, folding, and gluing. Notably, the ISP device possesses a device sensitivity of 10 nF kPa−1 cm−2, which is thousands of times higher than that of the commercial counterpart, a resolution of 6.25 Pa, a single‐millisecond response time, and a high linearity (R
2 > 0.996). Benefiting from the unique properties of the fibrous paper structures and its remarkable performances, the ISP devices hold enormous potential for the emerging human–machine interfaces, including smart packaging, health wearables, and pressure‐sensitive paper matrix.
A flexible iontronic sensing paper with both ionic and conductive patterns as an all‐in‐one flexible sensing platform, with direct printability, custom cuttability, and 3D foldability is structured into a pressure‐sensing device by paper‐specific manipulations in the forms of a 2D device or a 3D tactile‐sensing‐enabled origami with remarkable sensitivity, resolution, response linearity, and response time.
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