Scalar Versions Research Articles

Two Schwarzschild-like black holes balanced by their scalar hair

We show that, unlike vacuum General Relativity, Einstein-scalar theories allow balanced static, neutral, asymptotically flat, double-black hole solutions, for scalar field models minimally coupled to gravity, with appropriate self-interactions. These are scalar hairy versions of the double-Schwarzschild (or Bach-Weyl) solution, but regular on and outside the two (topologically spherical) horizons. The balancing repulsive force is provided by the scalar field. An explicit illustration is presented, using a Weyl-type construction adapted to numerical solutions, requiring no partial linearisation, or integrability structure, of the Einstein-scalar equations. Fixing the couplings of the model, the balanced configurationsform a one-parameter family of solutions, labelled by the proper distance between the black holes.

Three-axis isotropic-sensitivity He4 magnetometer with alignment-based longitudinal parametric resonance

For measurements in near-zero magnetic fields, vector atomic magnetometers are promising alternatives to scalar versions, but generally suffer from inconsistent performance over three axes. We present a single-beam vector magnetometer with three-axis isotropic sensitivity based on $^{4}\mathrm{He}$ atomic alignment. Longitudinal parametric resonance with atoms pumped by linearly polarized light is proposed for the $z$-axis measurement, while the Hanle effect in transverse geometry is used for $x$- and $y$-axis measurements. The evolution of atomic alignment multipole components and expressions of the three-axis magnetic responses are analyzed in detail. We describe the experimental operation of the proposed magnetometer with a magnetic-field noise floor of $150\phantom{\rule{0.16em}{0ex}}\mathrm{fT}/{\mathrm{Hz}}^{1/2}$ for the three axes, which is attractive for biomagnetism requiring vector characterization and source reconstruction.

A Novel Multistep Iterative Technique for Models in Medical Sciences with Complex Dynamics.

This paper proposes a three-step iterative technique for solving nonlinear equations from medical science. We designed the proposed technique by blending the well-known Newton's method with an existing two-step technique. The method needs only five evaluations per iteration: three for the given function and two for its first derivatives. As a result, the novel approach converges faster than many existing techniques. We investigated several models of applied medical science in both scalar and vector versions, including population growth, blood rheology, and neurophysiology. Finally, some complex-valued polynomials are shown as polynomiographs to visualize the convergence zones.

Development of a New Multi‐step Iteration Scheme for Solving Non‐Linear Models with Complex Polynomiography

The appearance of nonlinear equations in science, engineering, economics, and medicine cannot be denied. Solving such equations requires numerical methods having higher‐order convergence with cost‐effectiveness, for the equations do not have exact solutions. In the pursuit of efficient numerical methods, an attempt is made to devise a modified strategy for approximating the solution of nonlinear models in either scalar or vector versions. Two numerical methods of second‐and sixth‐order convergence are carefully merged to obtain a hybrid multi‐step numerical method with twelfth‐order convergence while using seven function evaluations per iteration, resulting in the efficiency index of about 1.4262. The convergence is also ascertained theoretically, and the asymptotic error constant is computed. Furthermore, various numerical methods of varying orders are used to compare the numerical results obtained with the proposed hybrid method in approximate solution, number of iterations, absolute error, absolute functional value, and the machine time measured in seconds. The obtained results outperformed the chosen methods when applied models arising from physical and natural fields were solved. Finally, to observe the convergence graphically, some complex polynomials are plotted as polynomiographs, wherein the rapid convergence of the proposed method is guaranteed.

Thermodynamics and geometrothermodynamics of Reissner-Nordström black holes in multidimensional power-law models

This article analyzes the geometric properties of the equilibrium variety of black holes on the background of a higher-dimensional model. Models with power-law dependence of multidimensional black hole models are considered as a special case. This work provides a general overview of the work on this topic. The main components of the formalism of geometric thermodynamics are considered and thermodynamics for this metric is presented, which is used here to analyze the equilibrium variety of configurations of black holes. The main part of this study is the consideration of a particular case for the study of thermodynamics and geometrothermodynamics of the Reissner-Nordstrom five-dimensional black hole in a gravitational field. For the five-dimensional Reissner-Nordström black hole, singularity points are determined at which second-order phase transitions occur, which show interactions in a gravitational field. It is shown that the manifestation of the curvature of the considered black hole with phase transitions occurring in it demonstrates its behavior in a gravitational field. It should be noted that the structure of the phase transition of a black hole may depend on the chosen model of the ensemble. Consequently, the only features in all considered scalar versions of curvature in the representation of entropy, mass and enthalpy, depending on thermodynamic parameters, arise from beyond the limits of applicability of the thermodynamic approach to a black hole, where it is assumed that it is impossible to apply the usual approaches of general relativity.

Further refinements of Young’s type inequality for positive linear maps

In this work, we give a multiple-term refinement of Young’s inequality which allow us to generalize and unify several results. As applications, we provide further refinements of a reversed AM–GM operator inequalities which extends and unifies two recent and important results due to Yang et al. (Math Slovaca 69:919–930, 2019) and Ren et al. (J Inequal Appl 2020:98, 2020) for positive linear maps and matrices. Also, our work deals with several other related results to both scalar and operator versions of the generalized Young’s inequality. In particular, we give a multiple-term refinement of Young’s inequalities for Hilbert–Schmidt norm, the determinants and the traces of positive definite matrices.

A codex on linearized Nordstr\xf6m supergravity in eleven and ten dimensional superspaces

As the full off-shell theories of supergravity in the important dimensions of eleven and ten dimensions are currently unknown, we introduce a superfield formalism as a foundation and experimental laboratory to explore the possibility that the scalar versions of the higher dimensional supergravitation theory can be constructed.

Rortex and comparison with eigenvalue-based vortex identification criteria

Most of the current Eulerian vortex identification criteria, including the Q criterion and the λci criterion, are exclusively determined by the eigenvalues of the velocity gradient tensor or the related invariants and thereby can be regarded as eigenvalue-based criteria. However, these criteria will be plagued with two shortcomings: (1) these criteria fail to identify the swirl axis or orientation; (2) these criteria are prone to severe contamination by shearing. To address these issues, a new vector named Rortex which represents the local fluid rotation was proposed in our previous work. In this paper, an alternative eigenvector-based definition of Rortex is introduced. The direction of Rortex, which represents the possible axis of the local rotation, is determined by the real eigenvector of the velocity gradient tensor. And then the rotational strength obtained in the plane perpendicular to the possible axis is used to define the magnitude of Rortex. This new equivalent definition allows a much more efficient implementation. Furthermore, a systematic interpretation of scalar, vector, and tensor versions of Rortex is presented. By relying on the tensor interpretation, the velocity gradient tensor is decomposed to a rigid rotation part and a non-rotational part including shearing, stretching, and compression, different from the traditional symmetric and anti-symmetric tensor decomposition. It can be observed that shearing always manifests its effect on the imaginary part of the complex eigenvalues and consequently contaminates eigenvalue-based criteria, while Rortex can exclude the shearing contamination and accurately quantify the local rotational strength. In addition, in contrast to eigenvalue-based criteria, not only the iso-surface of Rortex but also the Rortex vectors and the Rortex lines can be applied to investigate vortical structures. Several comparative studies on simple examples and realistic flows are studied to confirm the superiority of Rortex.

New progress on the operator inequalities involving improved Young\u2019s and its reverse inequalities relating to the Kantorovich constant

The purpose of this paper is to give a survey of the progress, advantages and limitations of various operator inequalities involving improved Young’s and its reverse inequalities related to the Kittaneh-Manasrah inequality. We also present our new progress to the related research topics. New scalar versions of Young’s inequalities are promoted, the operator version and the Hilbert-Schmidt form also get a promotion.

Buckling on stanene: the role played by spin-orbit coupling and pseudo Jahn-Teller effect

ABSTRACTTwo-dimensional group IV layers beyond graphene, as silicene, germanene and the Sn-based stanene, have been recently synthesized by molecular beam epitaxy. Density Functional Theyory (DFT) calculations predict low-buckled structures for these 2D nanosheets, with a hexagonal honeycomb conformation, typical of the graphene-like surfaces. The buckling parameter δ increases from Si to Sn-based layers, with a maximum predicted of 0.92 Å for stanene. High-buckled structures for these materials resulted to be unstable. We have previously shown that for silicene and germanene, the origin of the buckled structure resides on the pseudo Jahn-Teller puckering distortion, resulting from non-adiabatic effects. It has been shown that hexagermabenzene, the single hexagonal unit of germanene, is subject to a strong vibronic coupling whose origin is the pseudo Jahn-Teller effect. This coupling resulted to be around ten times larger than the one obtained for hexasilabenzene. For stanene, an additional effect needs to be considered to understand the origin of buckling: the spin-orbit coupling (SOC). This SOC contributes to open an electronic band gap, enabling the use of these layers as nanoelectronic components. In this work, we present an analysis based on DFT in the Zeroth-Order Regular Approximation (ZORA) for both scalar relativistic and spin-orbit versions that quantify the influence of the spin-orbit coupling in the puckering of Sn6H6. Also, under the linear vibronic coupling model between the ground and the lowest excited states, we present the pseudo Jahn-Teller contribution. The scalar ZORA approximation is used to perform time-dependent DFT calculations to incorporate the low-energy excitations contributions. Our model leads to the determination of the coupling constants and predicts simultaneously the Adiabatic Potential Energy Surface behavior for the ground and excited states around the maximum symmetry point. These values allow us to compare the Jahn-Teller relevance in buckling with the other group IV layers.

Short-term forecast of daily curves of electricity demand and price

The features of the electricity, as well as the rules of the competitive electricity markets, create the need of accurate predictions of electricity demand and price in order to anticipate decisions. Mainly, the prediction task in energy markets has been studied in the literature with the aim of obtaining scalar (hourly, daily, …) forecasts given scalar (and/or, less frequently, functional) historical data. This paper provides two methods to predict next-day electricity demand and price daily curves given information from past curves. They are based on using robust functional principal component analysis and nonparametric models with functional both response and covariate. In addition, the nonparametric proposal is extended to incorporate, in a linear way, exogenous scalar covariates. Results of these methods for the electricity market of mainland Spain, in year 2012, are reported. Their accuracy is compared with that of a naïve method as well as with the corresponding to combining forecasts. Scalar versions are also included in the comparative study. This work extends and complements the methods and results in Vilar et al. (2012), focused on scalar forecasts.

Baire classes of affine vector-valued functions

We investigate Baire classes of strongly affine mappings with values in Fr\'echet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki's result on affine functions of the first Baire class is related to the approximation property of the range space. We further extend several results known for scalar functions on Choquet simplices or on dual balls of $L_1$-preduals to the vector-valued case. This concerns, in particular, affine classes of strongly affine Baire mappings, the abstract Dirichlet problem and the weak Dirichlet problem for Baire mappings. Some of these results have weaker conclusions than their scalar versions. We also establish an affine version of the Jayne-Rogers selection theorem.

Flexibility in MOFs: do scalar and group-theoretical counting rules work?

We investigate the ability of counting rules drafted from engineering to predict the flexibility or rigidity of bar-and-joint or body-and-joint assemblies representing metal organic frameworks. We show that while scalar counting rules are not reliable, group-theoretical approaches are able to disentangle mechanisms from states of self-stress and to predict the existence of flexible mechanisms. We give several detailed examples of such calculations, highlighting the fact that behind an abstract exterior they are in fact easy to apply and similar to the method used to obtain molecular vibrations. We also correct a slight misinterpretation of the rigidity of IRMOF-1.

Dynamic gradient models for the sub-grid scale stress tensor and scalar flux vector in large eddy simulation

ABSTRACTA number of dynamic variants of the modulated gradient model (MGM) for the sub-grid scale (SGS) stress tensor and the SGS scalar flux vector are developed and evaluated a posteriori in large eddy simulations of neutral and stably stratified turbulent channel flow. Two dynamic procedures are evaluated: one based on the local equilibrium hypothesis (called local-dynamic models) and one based on the global equilibrium and steady state hypotheses (global-dynamic models). These local-dynamic (LD) and global-dynamic (GD) versions of MGM are found to be much more accurate than the constant coefficient MGM in neutral turbulent channel flow at friction Reynolds numbers of 180 and 590. The constant coefficient MGM and GD-MGM are also found to yield the correct asymptotic behaviour close to the wall, which indicates the suitability of coupling the MGM kernel with the GD procedure. For the SGS scalar flux vector, LD and GD versions of the MGM are evaluated along with LD and GD versions of the recently proposed Smagorinsky-gradient (SGM) and Vreman-gradient (VGM) models. Tests in neutral and stably stratified channel flow at friction Reynolds number of 180 and friction Richardson numbers of 0 and 18 reveal that all six dynamic SGS scalar flux vector models are able to reproduce first-order and second-order turbulent statistics accurately. The simulations help further establish the stability and accuracy of SGM and VGM, which have not been tested previously. None of the dynamic gradient-based SGS scalar flux vector models are found to yield the correct asymptotic behaviour, however, and this issue needs further investigation.

A Generalized Functional Model Based Method for Vibration-Based Damage Precise Localization in 3D Structures

A Generalized Functional Model Based Method for vibration-based damage precise localization on structures consisting of 1D, 2D, or 3D elements is introduced. The method generalizes previous versions applicable to structures consisting of 1D elements, thus allowing for 2D and 3D elements as well. It is based on scalar (single sensor) or vector (multiple sensor) Functional Models which - in the inspection phase - incorporate the mathematical form of the specific structural topology. Precise localization is then based on coordinate estimation within this model structure, and confidence bounds are also obtained. The effectiveness of the method is demonstrated through experiments on a 3D truss structure where damage corresponds to single bolt loosening. Both the scalar and vector versions of the method are shown to be effective even within a very limited, low frequency, bandwidth of 3-59 Hz. The improvement achieved through the use of multiple sensors is also demonstrated.

A note on the equivalence of some metric and H-cone metric fixed point theorems for multivalued contractions

AbstractIn this paper, by using Minkowski functional introduced by Kadelburg et al. (Appl. Math. Lett. 24:370-374, 2011) or nonlinear scalarization function introduced by Du (Nonlinear Anal. 72:2259-2261, 2010), we prove some equivalences between vectorial versions of fixed point theorems for H-cone metrics in the sense of Arshad and Ahmad and scalar versions of fixed point theorems for (general) Hausdorff-Pompeiu metrics (in usual sense).

Symbolic Crosschecking of Data-Parallel Floating-Point Code

We present a symbolic execution-based technique for cross-checking programs accelerated using SIMD or OpenCL against an unaccelerated version, as well as a technique for detecting data races in OpenCL programs. Our techniques are implemented in KLEE-CL, a tool based on the symbolic execution engine KLEE that supports symbolic reasoning on the equivalence between expressions involving both integer and floating-point operations. While the current generation of constraint solvers provide effective support for integer arithmetic, the situation is different for floating-point arithmetic, due to the complexity inherent in such computations. The key insight behind our approach is that floating-point values are only reliably equal if they are essentially built by the same operations. This allows us to use an algorithm based on symbolic expression matching augmented with canonicalisation rules to determine path equivalence. Under symbolic execution, we have to verify equivalence along every feasible control-flow path. We reduce the branching factor of this process by aggressively merging conditionals, if-converting branches into select operations via an aggressive phi-node folding transformation. To support the Intel Streaming SIMD Extension (SSE) instruction set, we lower SSE instructions to equivalent generic vector operations, which in turn are interpreted in terms of primitive integer and floating-point operations. To support OpenCL programs, we symbolically model the OpenCL environment using an OpenCL runtime library targeted to symbolic execution. We detect data races by keeping track of all memory accesses using a memory log, and reporting a race whenever we detect that two accesses conflict. By representing the memory log symbolically, we are also able to detect races associated with symbolically-indexed accesses of memory objects. We used KLEE-CL to prove the bounded equivalence between scalar and data-parallel versions of floating-point programs and find a number of issues in a variety of open source projects that use SSE and OpenCL, including mismatches between implementations, memory errors, race conditions and a compiler bug.

Constrained Hamiltonian Monte Carlo in BEKK GARCH with Targeting

AbstractThe GARCH class of models for dynamic conditional covariances trades off flexibility with parameter parsimony. The unrestricted BEKK GARCH dominates its restricted scalar and diagonal versions in terms of model fit, but its parameter dimensionality increases quickly with the number of variables. Covariance targeting has been proposed as a way of reducing parameter dimensionality, but for the BEKK with targeting the imposition of positive definiteness on the conditional covariance matrices presents a significant challenge. In this article, we suggest an approach based on Constrained Hamiltonian Monte Carlo that can deal effectively both with the nonlinear constraints resulting from BEKK targeting and the complicated nature of the BEKK likelihood in relatively high dimensions. We perform a model comparison of the full BEKK and the BEKK with targeting, indicating that the latter dominates the former in terms of marginal likelihood. Thus, we show that the BEKK with targeting presents an effective way of reducing parameter dimensionality without compromising the model fit, unlike the scalar or diagonal BEKK. The model comparison is conducted in the context of an application concerning a multivariate dynamic volatility analysis of a foreign exchange rate returns portfolio.

Comparison and union of the Temple and Bazley lower bounds

The Lehmann-Maehly approach and Bazley’s method of special choice are matrix eigenvalue problems that allow the calculation of lower bounds to energies of atomic and molecular systems. We introduce a common derivation of their scalar versions using the overlap of a trial function with the unknown ground-state wave function. In the scalar setting, the Lehmann-Maehly approach reduces to the Temple formula. The common derivation allows us to easily unite and improve both methods in several stages within this restricted application. Finally we offer a different union that allows generalization to arbitrary dimension matrix methods. Calculations on the helium atom ground state illustrate the improvements and mergers.

Fixed point theorem of generalized operator quasi-contractive mapping in cone metric space

In this paper, we use bounded linear operators and the convexity in Banach space, introduce a new generalized operator quasi-contractive condition, prove a new fixed point theorem in cone metric space. The conclusion in this paper unify, improve and generalize many contractive-type and quasi-contractive-type fixed point theorems in metric spaces and cone metric spaces. A example is given, which explains that the operator versions contractive condition is real generalization of scalar versions contractive condition.