Projection Of Vector Research Articles

Classification of Vector Fields and Soliton Structures on a Tangent Bundle with a Ricci Quarter-Symmetric Metric Connection

Consider $TM$ as the tangent bundle of a (pseudo-)Riemannian manifold $M$, equipped with a Ricci quarter-symmetric metric connection $\overline{\nabla }$. This research article aims to accomplish two primary objectives. Firstly, the paper undertakes the classification of specific types of vector fields, including incompressible vector fields, harmonic vector fields, concurrent vector fields, conformal vector fields, projective vector fields, and $% \widetilde{\varphi }(Ric)$ vector fields, within the framework of $\overline{% \nabla }$ on $T\dot{M}$. Secondly, the paper establishes the necessary and sufficient conditions for the tangent bundle $TM$ to become as a Riemannian soliton and a generalized Ricci-Yamabe soliton with regard to the connection $\overline{\nabla }$.

Detection and Estimation of Diffuse Signal Components Using the Periodogram

One basic limitation of using the periodogram as a frequency estimator is that any of its significant peaks may result from a diffuse (or spread) frequency component rather than a pure one. Diffuse components are common in applications such as channel estimation, in which a given periodogram peak reveals the presence of a complex multipath distribution (unresolvable propagation paths or diffuse scattering, for example). We present a method to detect the presence of a diffuse component in a given peak based on analyzing the projection of the data vector onto the span of the signature’s derivatives up to a given order. Fundamentally, a diffuse component is detected if the energy in the derivatives’ subspace is too high at the peak’s frequency, and its spread is estimated as the ratio between this last energy and the peak’s energy. The method is based on exploiting the signature’s Vandermonde structure through the properties of discrete Chebyshev polynomials. We also present an efficient numerical procedure for computing the data component in the derivatives’ span based on barycentric interpolation. The paper contains a numerical assessment of the proposed estimator and detector.

Proton Decay and Gauge Coupling Unification in an Extended SU(5) GUT with 45D Higgs

Abstract We present a comprehensive study of an extended SU(5) grand unified theory (GUT) that incorporates a 45D Higgs representation to address the shortcomings of the minimal SU(5) GUT, such as the inability to generate realistic fermion mass hierarchies and insufficient proton stability. By considering a hierarchical mass spectrum for the scalar components of the 45D Higgs, we demonstrate that successful gauge coupling unification (GCU) can be achieved. The color octet scalar, color triplet scalar, and color antitriplet scalar play crucial roles in realizing GCU when their masses are significantly lighter than other components of the 45D Higgs. We focus on the proton decay channels mediated by the exchange of the color antitriplet scalar. Assuming that the 45D Higgs couples to all three generations of fermions, we determine the 45D Higgs Yukawa couplings with which the observed fermion mass matrices at low energies are realized. We calculate proton decay rates using the Yukawa couplings obtained from renormalization group evolutions and matching conditions at the GUT scale, thereby exploring the dependence of proton decay rates on model parameters. We find that the $p \rightarrow \nu \pi$ mode imposes the most stringent constraint on the mass of the color antitriplet scalar $M_{S_1}$. We also study the correlations between the lower bounds on $M_{S_1}$ derived from different proton decay modes.

Projective Vector Fields on Semi-Riemannian Manifolds

This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function ψ and the vector field ζ dual to dψ does not change its causal character, then P is homothetic, or ζ is a light-like vector field. Additionally, it is shown that a complete Riemannian manifold admits a projective vector field that is also conformal and non-Killing if and only if it is locally Euclidean. The paper also presents other results related to the characterization of Killing and parallel vector fields using the Ricci curvature and the Hessian of the function given by the inner product of the vector field.

A novel sensitivity analysis method for multi-input-multi-output structures considering non-probabilistic correlations

In practical engineering, a multi-input-multi-output (MIMO) structure generally features a significant number of correlated input parameters and output responses. Sensitivity analysis is usually adopted to select key parameters for improving the computational efficiency of structural analysis and design processes. Traditional sensitivity analysis methods based on probabilistic models for MIMO structures may not reliably and efficiently derive the sensitivity indexes of correlated input parameters with limited samples. To solve the above problems, a novel sensitivity analysis method for MIMO structures considering non-probabilistic correlations is proposed to estimate the influence of uncertainties and correlations among the parameters on the responses in a unified framework. Firstly, a multidimensional parallelepiped (MP) model is employed to quantify the uncertainties and non-probabilistic correlations among the parameters. A new non-probabilistic variance propagation equation based on the MP model is then proposed to derive the non-probabilistic variances of output responses. The non-probabilistic independent, correlated, and total sensitivity indexes of each parameter for multi-input-single-output (MISO) structures are defined according to the non-probabilistic variance contribution rates. A dimensional normalization method and a vector projection method are then adopted to extend the non-probabilistic sensitivity indexes of each parameter for MIMO structures with correlations. Two numerical examples and an experimental example are exemplified to verify the proficiency and efficiency of the currently proposed method.

Spontaneous CP violation in supersymmetric QCD

We investigate a composite model of spontaneous CP violation based on a new supersymmetric QCD as a solution to the strong CP problem. The scalar components of the meson chiral superfields obtain complex vacuum expectation values to break CP symmetry spontaneously. Then, wavefunction renormalization for the quark kinetic terms provides the Cabibbo-Kobayashi-Maskawa (CKM) phase, while the strong CP phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} is protected by nonrenormalization of the superpotential and hermiticity of the wavefunction renormalization factor. In our model, the right-handed down-type quark multiplets are given by composite states, enhancing their couplings to CP breaking fields, which is essential to realize the observed CKM phase. The non-perturbative dynamics generates the scale of spontaneous CP violation hierarchically lower than the Planck scale. We discuss potential corrections to θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} and find a viable parameter space of the model to solve the strong CP problem without fine-tuning.

On the conformal limit of a QED-inspired model

A conformal invariant QED-inspired model is solved for a general covariant linear gauge using the Dyson–Schwinger equations for the propagators assuming a pure vector like interaction. The leading corrections to the asymptotic solutions and the exponents, that characterize the corrections to each of the two fermion propagator functions, are computed as a function of the coupling and gauge fixing parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. For the scalar component of the fermion propagator our findings generalizes for linear covariant gauges previous results found in the literature and reproduce the outcome of the perturbative analysis of quenched QED in the Landau gauge. Our solution for the exponent associated with vector component of the fermion propagator is new and, in the weak coupling regime, agrees with the estimation based on the perturbative analysis of quenched QED. Of the two critical exponents describing the conformal limit of the vector interaction, one of them is, in QED, associated with the regime where chiral symmetry is broken dynamically, which demands one mass scale, namely the Miransky scaling. A second mass scale has to be introduced at larger coupling constants and is associated with a change on the nature of the fermion wave function. This provides one example, that it is possible to find two interwoven cycles in Quantum Field Theory, albeit in a truncated framework, as it is known in the quantum few-body problem in the limit of a zero-range interaction.

Cascade Ξ0 baryon spectroscopy in the relativistic framework of an independent quark model

The spectroscopy of Ξ0 is performed within the relativistic framework of independent quark model. The equal mixture of scalar and vector components in the potential having Martin-like form is considered for the confinement. With the suitable potential parameters for Ξ0, mass spectra for high radial and orbital excitation is calculated. The experimentally observed values of the ground-state magnetic moment, branching ratios, and asymmetry parameters for radiative weak decays, Ξ0→Λ0+γ0 and Ξ0→Σ0+γ0 are obtained to validate the model. The spin parity of experimentally known resonances like Ξ(1530), Ξ(1820), and Ξ(2030) are confirmed through the Regge trajectories in (J,M2) plane. The spin parity of Ξ(1950), Ξ(2130), and Ξ(2250) are predicted using those Regge trajectories. The radiative decay width and magnetic moment of first resonance is also predicted. Published by the American Physical Society 2024

Mode-Specific Dynamics Studies for the Multichannel C2H2 + OH Reaction.

The C2H2 + OH reaction is a key elementary reaction in acetylene oxidation, and the products forming in different reaction channels, such as C2H and CH3 radicals, are also important for subsequent reaction processes in the combustion process. In this work, we investigated the dynamics of the C2H2 + OH reaction with specific vibrational mode excitations and analyzed the mode specificity based on quasi-classical trajectory calculations on a recently developed full-dimensional potential energy surface. It is found that exciting OH stretching mode can promote the production of H + OCCH2 and CO + CH3, while the excitation of C-H symmetric/antisymmetric stretching mode of C2H2 can facilitate the H2O + C2H channel. Based on the prediction of vibrationally adiabatic and sudden vector projection models, the mode specificity in the C2H2 + OH reaction can be attributed to the difference in the degree of coupling between the initial motion mode and the reaction coordinate of each reaction path, which ultimately leads to the changes in rate constants and the product branching ratios. These findings can offer theoretical insights to regulate the branching ratio of the multichannel C2H2 + OH reaction.

Conformal 3D Printing Algorithm for Surfaces and Its In Situ Repair Applications.

Conformal 3D printing can construct specific three-dimensional structures on the free-form surfaces of target objects, achieving in situ additive manufacturing and repair, making it one of the cutting-edge technologies in the current field of 3D printing. To further improve the repair efficacy in tissue engineering, this study proposes a conformal path planning algorithm for in situ printing in specific areas of the target object. By designing the conformal 3D printing algorithm and utilizing vector projection and other methods, coordinate transformation of the printing trajectory was achieved. The algorithm was validated, showing good adherence of the printing material to the target surface. In situ repair experiments were also conducted on human hands and pig tibia defect models, verifying the feasibility of this method and laying a foundation for further research in personalized medicine and tissue repair.

Energy Barriers for the Spontaneous Magnetization Reversal of the Atomic Co Chains on Pt(664) Surface in the Model with Dzyaloshinskii–Moriya Interaction

The analytical approach has been developed in the framework of the continuous XY-model. This approach allows calculating the spontaneous magnetization reversal time of finite-length atomic chains on the metallic surface. The interaction of the magnetic moments of atoms is described by the classical Hamiltonian, which includes the Heisenberg exchange interaction, the Dzyaloshinskii–Moriya interaction, and the magnetic anisotropy energy. Using the Co/Pt(664) system as an example, it has been shown that the proposed method is in a good agreement with the results of the numerical simulation in the limit of short and long atomic chains. And for atomic chains of intermediate length, it can be used to estimate an upper bound on the spontaneous magnetization reversal time. We obtained the dependences of the spontaneous magnetization reversal time of finite-length Co chains the value of the exchange integral, parameters of the magnetic anisotropy, and also on the value of the projection of the Dzyaloshinskii vector onto the axis perpendicular to the plane containing the magnetic moments of the atoms. It is shown that the proposed method has a wide range of applicability both in terms of temperature and the values of the physical parameters characterizing the magnetic properties of the atomic chains.

Strategic analysis of intelligent connected vehicle industry competitiveness: a comprehensive evaluation system integrating rough set theory and projection pursuit

As a carrier of multi-industrial technology integration and the key to industrial competition, the intelligent connected vehicle (ICV) has been taken seriously around the world. However, as a fast-growing emerging industry, its development process varies greatly from place to place. Hence, the merits and demerits are analyzed for the development of the ICV industry in different cities scientifically and to clarify the development of different links in each city, this paper suggests an extensive assessment framework integrating rough set theory and projection pursuit-based computation to systematically assess and thoroughly evaluate the level of competitiveness of the ICV industry. First, through big data text analysis technology, we constructed a "5 + 24" two-tier evaluation index system composed of 24 level-II evaluation indexes as well as five level-I evaluation indexes and selected 19 typical cities as input data for the comprehensive evaluation system. Further, the Adaptive Random Forest based Crossover Tactical Unit (ARF-CTU) algorithm is proposed for evaluating the performance of the industrial vehicle industry. However, the ARF algorithm is employed to estimate the lowering of overfitting issues and handling of high dimensional data. Moreover, the continuously varying conditions are analyzed by CTU. Then, we constructed a comprehensive evaluation system in the rough set theory and projection pursuit: (I) Quoting the rough set non-decision-making algorithm for attribute reduction, that is, under the premise of unchanged classification ability, derive a new evaluation system, and calculate the index weight and score based on the new system. (II) Based on the projection pursuit technology, the index score is mapped by a genetic algorithm to a linear structure, and a one-dimensional projection vector is an output.

Four-derivative Yang-Mills couplings in heterotic theory through T-duality

This study delves into the dimensional reduction of the classical effective action of heterotic string theory on a circle, along with its T-duality symmetry, with the aim of identifying the bosonic couplings. To achieve this, we propose a truncation scheme for the generalized Buscher rules and the reduced action, specifically targeting the truncation of the nonlinear appearance of the scalar component of the Yang-Mills field in the base space. By imposing this truncated T-duality on the reduced action, we successfully determine the four- derivative bosonic couplings in the minimal basis, where field redefinition is imposed. Notably, these couplings, which are associated with the Lorentz Chern-Simons coupling HΩ, exhibit an exact correspondence with the NS-NS couplings found in the Metsaev-Tseytlin action.Furthermore, we investigate the bosonic couplings in the maximal basis, where field redefinition is not imposed. In this scenario, the truncated T-duality fixes the effective action up to 17 arbitrary parameters. By assigning specific values to these parameters, we establish a framework in which the NS-NS couplings align with those in the Meissner action. Remarkably, within this scheme, the Yang-Mills couplings precisely coincide with those obtained through the S-matrix method.

StraitFlux – precise computations of water strait fluxes on various modeling grids

Abstract. Oceanic transports shape the global climate, but the evaluation and validation of this key quantity based on reanalysis and model data are complicated by the distortion of the used curvilinear ocean model grids towards their displaced north poles. Combined with the large number of different grid types, this has made the exact calculation of oceanic transports a challenging and time-consuming task. Use of data interpolated to standard latitude/longitude grids is not an option, since transports computed from interpolated velocity fields are not mass-consistent. We present two methods for transport calculations on grids with variously shifted north poles, different orientations, and different Arakawa partitions. The first method calculates net transports through arbitrary sections using line integrals, while the second method generates cross sections of the vertical–horizontal planes of these sections using vector projection algorithms. Apart from the input data on the original model grids, the user only needs to specify the start and endpoints of the required section to get the net transports (for the first method) and their cross sections (for the second method). Integration of the cross sections along their depth and horizontal extent yields net transports in very good quantitative agreement with the line integration method. This allows us to calculate oceanic fluxes through almost arbitrary sections to compare them with observed oceanic volume and energy transports at available sections, such as the RAPID array or at Fram Strait and other Arctic gateways, or to compare them amongst reanalyses and to model integrations from the Coupled Model Intercomparison Projects (CMIPs). We implemented our methods in a Python package called StraitFlux. This paper represents its scientific documentation and demonstrates its application on outputs of multiple CMIP6 models and several ocean reanalyses. We also analyze the robustness and computational performance of the tools, as well as the uncertainties in the results. The package is available on GitHub and Zenodo and can be installed using pypi.

A Closed Formalism for Anatomy-Independent Projection and Optimization of Magnetic Stimulation Coils on Arbitrarily Shaped Surfaces.

Transcranial magnetic stimulation (TMS) is a popular method for the noninvasive stimulation of neurons in the brain. It has become a standard instrument in experimental brain research and has been approved for a range of diagnostic and therapeutic applications. These applications require appropriately shaped coils. Various applications have been established or approved for specific coil designs with their corresponding spatial electric field distributions. However, the specific coil implementation may no longer be appropriate from the perspective of available material and manufacturing opportunities or considering the latest understanding of how to achieve induced electric fields in the head most efficiently. Furthermore, in some cases, field measurements of coils with unknown winding or a user-defined field are available and require an actual implementation. Similar applications exist for magnetic resonance imaging coils. This work aims at introducing a complete formalism free from heuristics, iterative optimization, and ad-hoc or manual steps to form practical stimulation coils with individual turns to either equivalently match an existing coil or produce a given field. The target coil can reside on practically any sufficiently large or closed surface adjacent to or around the head. The method derives an equivalent field through vector projection exploiting the well-known Huygens' and Love's equivalence principle. In contrast to other coil design or optimization approaches recently presented, the procedure is an explicit forward Hilbert-space vector projection or basis change. For demonstration, we map a commercial figure-of-eight coil as one of the most widely used devices and a more intricate coil recently approved clinically for addiction treatment (H4) onto a bent surface close to the head for highest efficiency and lowest field energy. The resulting projections are within ≤4% of the target field and reduce the necessary pulse energy by more than 40%.

Spin-orbital conversion of the light field immediately behind an ideal spherical lens

The Richards-Wolf equations not only adequately describe a light field distribution at the sharp focus, but are also able to describe a light field distribution just behind an ideal spherical lens, i.e. on a converging spherical wavefront. Knowing all projections of light field strength vectors behind the lens, longitudinal components of the spin angular momentum and orbital angular momentum (SAM and OAM) can be derived. In this case, the longitudinal projection of the SAM just behind the lens either remains zero or decreases. This means that the spin-orbital conversion (SOC), where part of the “spin transfers orbit”, occurs just behind the ideal spherical lens. Notably, the sum of the longitudinal projections of SAM and OAM is conserved. Regarding the spin Hall effect, it is revealed that rather than forming just behind the lens, it appears as focusing occurs. Thus, we find that while just behind the lens there is no Hall effect, it becomes maximally pronounced in the focal plane. It is because just behind the ideal spherical lens, two optical vortices with topological charges (TCs) –2 and 2 and opposite-sign spins (with right and left circular polarization) are generated. However, the total spin is equal to zero because the two vortices have the same amplitudes. The amplitudes of the optical vortices become different in the course of focusing and in the focal plane and, therefore, areas with opposite-sign spins (Hall effect) are formed. We also present a general form of the incident light fields whose longitudinal component is zero in the focal plane. In this case, the SAM vector can only have the longitudinal non-zero component. The notion of the SAM vector elongated only along the optical axis in the focal plane is applied for solving magnetization problems.

Global Supply Chain Disruptions, Commodity Price Shocks and Inflation in Japan

In recent years, the concurrent occurrences of the COVID-19 pandemic and the Russian invasion of Ukraine have led to global disruptions in supply chains and a surge in commodity prices. Major advanced economies have experienced an increase in inflation rates and a decline in economic activity. Against this economic backdrop, this paper aims to address the strained condition of supply chains by employing the Global Supply Chain Pressure Index (GSCPI) alongside commodity price indices. Furthermore, it seeks to examine how fluctuations in these variables affect Japan’s macroeconomic landscape through local projection and structural Vector Autoregression (VAR). In the local projection analysis, it has been observed that the strain on supply chains induces sustained increases in consumer and producer prices, further contributing to long-term declines in production. Within the structural VAR model framework, the identification of structural shocks is conducted through sign restrictions, affirming the significance of supply chain shocks and energy and food price shocks as crucial factors contributing to recent price increases. This confirmation is supported by variance decomposition and historical decomposition analyses.

Impact of new experimental data on the C2HDM: the strong interdependence between LHC Higgs data and the electron EDM

The complex two-Higgs doublet model (C2HDM) is one of the simplest extensions of the Standard Model with a source of CP-violation in the scalar sector. It has a \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{Z}}_{2}$$\\end{document} symmetry, softly broken by a complex coefficient. There are four ways to implement this symmetry in the fermion sector, leading to models known as Type-I, Type-II, Lepton-Specific and Flipped. In the latter three models, there is a priori the surprising possibility that the 125 GeV Higgs boson couples mostly as a scalar to top quarks, while it couples mostly as a pseudoscalar to bottom quarks. This “maximal” scenario was still possible with the data available in 2017. Since then, there have been more data on the 125 GeV Higgs boson, direct searches for CP-violation in angular correlations of τ-leptons produced in Higgs boson decays, new results on the electron electric dipole moment, new constraints from LHC searches for additional Higgs bosons and new results on b → sγ transitions. Highlighting the crucial importance of the physics results of LHC’s Run 2, we combine all these experiments and show that the “maximal” scenario is now excluded in all models. Still, one can have a pseudoscalar component in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h\ au \\overline{\ au }$$\\end{document} couplings in the Lepton-Specific case as large as 87% of the scalar component for all mass orderings of the neutral scalar bosons.

Complete EFT operator bases for dark matter and weakly-interacting light particle

The standard model can be extended to include weakly-interacting light particle (WILP): real or complex singlet scalar with a conserved U(1) charge, Majorana or Dirac neutral fermion, neutral or hidden-charged vector boson, etc. Imposing the Z2 symmetry, these particles can be lifted as the weakly-interacting massive particle (WIMP), the candidate of dark matter. Instead, imposing the shift symmetry on the scalar components gives rise to the axion-like particle, dark photon, etc. Utilizing these light degrees of freedom along with the standard model particles and imposing different symmetries, we construct the complete and independent sets of effective operators up to dimension eight with the Young tensor technique, consistent with counting from the Hilbert series.

Automorphisms of projective structures

We study the problem of classifying local projective structures in dimension two having non trivial Lie symmetries. In particular we obtain a classification of foliated projective structures having positive dimensional Lie algebra of projective vector fields.