Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model

In this paper, we investigate a feasible holography with the Kitaev model using dilatonic gravity in AdS2. We propose a generic dual theory of gravity in the AdS2 and suggest that this bulk action is a suitable toy model in studying quantum mechanics in Kitaev model using gauge/gravity duality. This gives a possible equivalent description for the Kitaev model in the dual gravity bulk. Scalar and tensor perturbations are investigated in details. In the case of near AdS perturbation, we show that the geometry still “freezes” as is AdS, while the dilation perturbation decays at the AdS boundary safely. The time-dependent part of the perturbation is an oscillatory model. We discover that the dual gravity induces an effective and renormalizable quantum action. The entanglement entropy for bulk theory is computed using extremal surfaces. We prove that these surfaces have a fold bifurcation regime of criticality.

On a generalization of principal weak (po-)flatness of S-posets

In [H. Rashidi, A. Golchin and H. Mohammadzadeh saany, On [Formula: see text]-flat acts, Categ. Gen. Algebr. Struct. Appl. 12(1) (2020) 175–197], the study of [Formula: see text]-flatness property of right acts [Formula: see text] over a monoid [Formula: see text] that can be described by means of when the functor [Formula: see text]-preserves some pullbacks is initiated. In this paper, we extend these results to [Formula: see text]-posets and present equivalent description of [Formula: see text]-po-flatness of [Formula: see text]-posets. We show that [Formula: see text]-flatness does not imply torsion freeness in [Formula: see text]-posets and give some general properties and a characterization of pomonoids for which some other properties of their posets imply this condition.

Characteristics of quantifiers moderate the framing effect

The attribute framing effect, where people judge a quantity of an item more positively with a positively-described attribute (e.g., ‘75% lean’) than its negative, albeit normatively equivalent description (e.g., ‘25% fat’), is a robust phenomenon, which may be moderated under certain conditions. In this paper, we investigated the moderating effect of the characteristics of the quantifier term: its format (verbal, e.g., ‘high’, or numerical, e.g., ‘75%’) and magnitude (i.e., if it is a small or large quantity) using positive or negative synonyms of attributes (e.g., energy vs. calories). Over five pre-registered studies using a 2 (synonym, between-subjects: positive or negative) 2 (quantifier format, between-subjects: verbal or numerical) 2 (quantifier magnitude, within-subjects: small or large) mixed design, we manipulated quantifier format and magnitude orthogonally for synonyms with differing valence. We also tested two mechanisms for the framing effect: whether the effect was mediated by the affect associated with the frame, and whether participants inferred the speaker to be positive about the target. We found a framing effect with synonyms that was reversed in direction for the small (vs. large) quantifiers, but not significantly moderated by quantifier format. Both the affect associated with the frame and the inferred level of speaker positivity partially mediated the framing effect, and the level of mediation varied with quantifier magnitude. These results suggest that the magnitude of the quantifier modifies one’s evaluation of the frame, and the mechanism for people’s evaluations in a framing situation may differ for small and large quantifiers.

Quantum SU(2|1) supersymmetric ℂN Smorodinsky-Winternitz system

We study quantum properties of SU(2|1) supersymmetric (deformed $$ \mathcal{N} $$ N = 4, d = 1 supersymmetric) extension of the superintegrable Smorodinsky-Winternitz system on a complex Euclidian space ℂN. The full set of wave functions is constructed and the energy spectrum is calculated. It is shown that SU(2|1) supersymmetry implies the bosonic and fermionic states to belong to separate energy levels, thus exhibiting the “even-odd” splitting of the spectra. The superextended hidden symmetry operators are also defined and their action on SU(2|1) multiplets of the wave functions is given. An equivalent description of the same system in terms of superconformal SU(2|1, 1) quantum mechanics is considered and a new representation of the hidden symmetry generators in terms of the SU(2|1, 1) ones is found.

Multisensor decentralized nonlinear fusion using adaptive cubature information filter

In nonlinear multisensor system, abrupt state changes and unknown variance of measurement noise are very common, which challenges the majority of the previously developed models for precisely known multisensor fusion techniques. In terms of this issue, an adaptive cubature information filter (CIF) is proposed by embedding strong tracking filter (STF) and variational Bayesian (VB) method, and it is extended to multi-sensor fusion under the decentralized fusion framework with feedback. Specifically, the new algorithms use an equivalent description of STF, which avoid the problem of solving Jacobian matrix during determining strong trace fading factor and solve the interdependent problem of combination of STF and VB. Meanwhile, A simple and efficient method for evaluating global fading factor is developed by introducing a parameter variable named fading vector. The analysis shows that compared with the traditional information filter, this filter can effectively reduce the data transmission from the local sensor to the fusion center and decrease the computational burden of the fusion center. Therefore, it can quickly return to the normal error range and has higher estimation accuracy in response to abrupt state changes. Finally, the performance of the developed algorithms is evaluated through a target tracking problem.

Degenerate Elastic Networks

We minimize a linear combination of the length and the $$L^2$$ L 2 -norm of the curvature among networks in $$\mathbb {R}^d$$ R d belonging to a given class determined by the number of curves, the order of the junctions, and the angles between curves at the junctions. Since this class lacks compactness, we characterize the set of limits of sequences of networks bounded in energy, providing an explicit representation of the relaxed problem. This is expressed in terms of the new notion of degenerate elastic networks that, rather surprisingly, involves only the properties of the given class, without reference to the curvature. In the case of $$d=2$$ d = 2 we also give an equivalent description of degenerate elastic networks by means of a combinatorial definition easy to validate by a finite algorithm. Moreover we provide examples, counterexamples, and additional results that motivate our study and show the sharpness of our characterization.

An equivalent description of the lens space L(p,q) with p prime

In the paper, we give an equivalent description of the lens space [Formula: see text] with [Formula: see text] prime in terms of any corresponding Heegaard diagrams as follows: Let [Formula: see text] be a closed orientable 3-manifold with [Formula: see text] and [Formula: see text] a Heegaard splitting of genus [Formula: see text] for [Formula: see text] with an associated Heegaard diagram [Formula: see text]. Assume [Formula: see text] is a prime integer. Then [Formula: see text] is homeomorphic to the lens space [Formula: see text] if and only if there exists an embedding [Formula: see text] such that [Formula: see text] bounds a complete system of surfaces for [Formula: see text].

The Effect of Geometry on Harmonically Varied Helix Milling Tools

Two different kinds of descriptions for edge geometry of harmonically varied helix tools are studied in this work. The edge geometries of the so-called lag and helix variations are used in this paper, and their equivalency is established from engineering point of view. The equivalent relation is derived analytically and the nonlinear algebraic system is described, with which the numerical equivalency properties can be determined. The equivalent description can be utilized in variable helix tool production to determine an optimized set of geometrical parameters of the edge geometry. The stability properties are shown and compared for a simple one degree-of-freedom case with the nonuniform constant helix tools. The robustness of the results related to the harmonically varied tools is critically discussed in this paper showing advantages compared to the nonuniform constant helix case. The results suggest that the more extreme the edge variation is, the more stable the process performed with the corresponding harmonically varied tool becomes.

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).

Exact Generalized Kohn-Sham Theory for Hybrid Functionals

p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; line-height: 18.0px; font: 15.8px Helvetica; color: #000000; -webkit-text-stroke: #000000; background-color: #ffffff} span.s1 {font-kerning: none} span.s2 {font-kerning: none; color: #000000} <p>Hybrid functionals have proven to be of immense practical value in density functional theory calculations. While they are often thought to be a heuristic construct, it has been established that this is in fact not the case. Here, we present a rigorous and formally exact generalized Kohn-Sham (GKS) density functional theory of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of Fock exchange to produce the correct ground state density. Specifically, we generalize the well-known adiabatic con- nection theorem to the case of exact hybrid functional theory and use it to provide a rigorous distinction between multiplicative exchange and correlation components. We examine the exact theory by inverting reference electron densities to obtain exact GKS potentials for hybrid functionals, showing that an equivalent description of the many-electron problem is obtained with any arbitrary global fraction of Fock exchange. We establish the dependence of these exact components on the fraction of Fock exchange and use the observed trends to shed new light on the results of approximate hybrid functional calculations.</p>