Continuity Assumption Research Articles

The Relations Between Hölder Continuity Assumptions on the Direction of Vorticity and Energy Equality

The Relations Between Hölder Continuity Assumptions on the Direction of Vorticity and Energy Equality

On the Implementation of Iterative Methods Without Inverse Updating for Solving Equations in Banach Spaces

The implementation of iterative methods using inverses to solve equations is a computationally expensive or impossible task in general. This is the case, since the analytical form of the inverse is difficult to find in practice. That is why, we replace the inverse by a sum of linear operators which is well defined. The convergence of the resulting hybrid methods is studied based on majorizing sequences under generalized continuity assumptions on the operators involved and in the setting of a Banach space. It is demonstrated by numerical experimentations that the convergence order as well as the number of iterations required to obtain a predetermined error tolerance when comparing the original to the hybrid method is essentially the same.

Water compression induced ionic negative differential resistance in nanopores.

The mass transport behavior through nanoscale channels, greatly influenced by the structures and dynamics of nanoconfined water, plays an essential role in many biophysical processes. However, the dynamics of nanoconfined water under an external field and its effects are still not fully understood. Here, on the basis of molecular dynamics simulations, we theoretically show that the ionic current of [Bmim][PF6] through narrow pores in graphene membrane exhibits an ionic negative differential resistance effect-the ionic current decreases as the voltage increases over a certain threshold. This effect arises from the violation of traditional fluid dynamics as the assumption of continuity and homogeneity of fluids is no longer effective in ultrathin nanopores. The gradient of electric field around the atomic-thin layer produces a strong gradient force on the polarized water inside the nanopore. This dielectrophoretically compressed water leads to a hydrostatic force that repels ions from entering the nanopore. Our findings may advance the understanding of hydrostatic mechanism, which governs ion transport through nanopores.

The generalized Łojasiewicz inequality for definable and subanalytic multifunctions

This paper is devoted to obtaining the Łojasiewicz inequality (version for two functions), in both the definable and subanalytic cases, under the most relaxed assumptions. It means that we drop the usual continuity and compactness assumptions. In the second part of the paper we concentrate on the Łojasiewicz inequality for multifunctions and apply it to the natural multifunctions related to the medial axis of a set (basic notion in pattern recognition).

Delayed Interval-Valued Symmetric Stochastic Integral Equations

In this paper, delayed stochastic integral equations with an initial condition and a drift coefficient given as interval-valued mappings are considered. These equations have a certain symmetric form that distinguishes them from classical single-valued stochastic integral equations and has implications for the properties of the diameter of the values of the solutions of the equations. The main result of the paper is the theorem that there is a unique solution to the equation considered. It was obtained under the assumptions of continuity of the kernels and Lipschitz continuity of the drift and diffusion coefficients. The proof of the existence of the solution is carried out by the method of iterating successive approximations. The paper ends with theorems about the continuous dependence of the solution on the initial function, kernels and nonlinearities.

A geometric view of seismic wavefields: implications for imaging dense clusters of events

SUMMARY Imaging dense clusters of seismicity is crucial to many problems in seismology: to delineate complex systems of faults, provide constraints on the causes of volcanic and cryogenic swarms, and to shed light on possible means to prevent damaging induced seismicity in mining, geothermal, and oil and gas extraction activities. Current imaging methods rely upon high-resolution relative location techniques, commonly requiring arrival-time picks for seismic phases. This paper examines an alternative approach, based upon concepts drawn from differential geometry, that images directly from waveform data. It relies upon the common assumption of spatial continuity of seismic wavefield observations, which implies that a differentiable map exists between the source region to be imaged and waveform observations considered as elements of a vector space. The map creates an image of event clusters on a Riemannian manifold embedded in that vector space. The image can be visualized by projecting the observations into a tangent space of the manifold and is a distorted rendering of cluster geometry. However, the distortion can be predicted and removed if a model for wavefield propagation is available. This visualization approach is applicable to clusters of uniform events with highly similar waveforms, such as are commonly acquired with correlation detectors or other pattern matching techniques. To assess its performance, it is applied to the closely related reciprocal problem of imaging the (known) geometry of an array from observations by the array of several regional events. Differences between the original problem and its reciprocal analogue are noted and controlled for in the analysis. Chief among the differences is the necessity for aligning the waveforms in the original problem, which, to maintain consistency with the original problem, is solved in the reciprocal problem by a generalization of the VanDecar–Crosson algorithm. The VanDecar–Crosson algorithm exhibits a bias, shown through an analysis of the situation when the observed wavefields are adequately modelled as plane waves. In that circumstance, the bias can be predicted and removed. In a test using a portion of a large-N array, this imaging approach is shown to successfully reconstruct the array geometry. The method is applicable directly to infinitesimal array apertures, but is extended to a larger aperture by partitioning the image into local, effectively infinitesimal overlapping subsets. These are inverted, then assembled into a global picture of the array geometry using constraints provided by the overlapped regions. Although demonstrated in a reciprocal array context, the method appears viable for imaging clusters of events with highly similar source mechanisms and time histories.

Unwrap Intractable C‐Band Coseismic Interferograms: An Improved SNAPHU Method With Range Offset Gradients as Prior Information

AbstractC‐band Interferometric Synthetic Aperture Radar (InSAR) data are widely used to map coseismic deformation. However, phase unwrapping errors are commonly distributed near faults owing to decorrelation and steep phase gradients from short radar wavelengths. Here, we propose an improved SNAPHU phase‐unwrapping algorithm that considers the prior information of the range offset gradients (P‐SNAPHU) to overcome the constraints imposed by the phase continuity assumption. P‐SNAPHU exploits median filtering of homogeneous pixels for initial denoising of range offset and then refines range offset gradients divisionally through saliency extraction. The derived gradients are used to estimate the expected values of the cost functions for the low‐coherence fringes. The synthetic experiments show significant improvements in the phase‐unwrapping accuracy of the P‐SNAPHU method compared with classical unwrapping methods. We apply the P‐SNAPHU method to unwrap Sentinel‐1 coseismic interferograms of three large (Mw > 6.5) strike‐slip earthquake events that the existing classical methods could not successfully unwrap. In the comparison of the unwrapped interferograms with the external global navigation satellite system (GNSS) displacements and those from the classical methods, we find that P‐SNAPHU significantly reduces the phase unwrapping errors with the mean absolute error of 7.2, 2.3, and 1.8 cm for the 2023 Kahramanmaraş earthquake doublet, the 2016 Kumamoto earthquake, and the 2019 Ridgecrest earthquakes, respectively. Based on the unwrapped results derived from P‐SNAPHU, an estimate is made regarding the shallow slip deficit of the 2023 Kahramanmaraş earthquake doublet, which is approximately 7%. Therefore, P‐SNAPHU is useful for developing and applying C‐band InSAR data for large earthquakes and volcanic activity.

A Modified Three-terms CG Method with the MWWP Line Search and its Application to Image Restoration

Abstract In this article, an innovative method, which integrates the optimized three-term Polak–Ribière–Polyak (PRP) conjugate gradient (CG) method with the improved WWP line search rule, is presented and applied in the field of image restoration. The proposed search direction exhibits sufficient descent and trust region characteristics, maintaining its effectiveness regardless of the specific line search rule employed. We established the global convergence of the presented algorithm and eliminated the dependence on the Lipschitz continuity assumption. The numerical comparisons with the PRP CG method revealed the superior performance of the designed algorithm in the field of image restoration. This research outcome provides strong support for further advancements in the field of image recovery.

We don’t need a science of animal consciousness. On the unexpected insights gained from Walter Veit’s “A philosophy for the science of animal consciousness”

This paper is a critical commentary on Walter Veit’s book "A philosophy for the science of animal consciousness." My goal is to show that although Veit succeeds in presenting a compelling account of animal consciousness, he may have unintentionally undermined the purpose of such science. I argue that, despite the author’s claims, his theory is not as empirically grounded as he makes it out to be. Paradoxically, some of Veit’s arguments against his opponents seem to be double-edged. Still, I also argue that this is a necessary cost, as an alternative would be to succumb to a particular form of metatheoretical anthropomorphism. In effect, we end up with a surprising conclusion that we need many sciences of different consciousnesses, which seems at odds with Veit’s Darwinian continuity assumption. However, this only goes to show that the book is well worth discussing.

Traveling wave vibration characteristic analysis of FRC sandwich cylindrical shells with FGP-GPLRC core under discontinuous elastic boundary conditions

In this study, a fiber-reinforced composite (FRC) sandwich cylindrical shell with a functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) core is investigated, and the traveling wave vibration characteristics of this new sandwich cylindrical shell under discontinuous elastic boundary conditions are analyzed for the first time. The influences of centrifugal and Coriolis forces are introduced into the model. By employing the first-order shear deformation theory (FSDT) and the continuity assumption of the layerwise theory, the governing equations of the rotating sandwich shell are obtained. The artificial springs are implemented at the ends of the sandwich shell to represent the discontinuous elastic boundary conditions. The natural frequency of the shell is solved via the Rayleigh-Ritz method and the state space method. Then, the approach proposed is validated by comparing the present results with those reported in the literature and the finite element method. Finally, the effects of various parameters on the traveling wave frequency of the shell are evaluated. It was found that in practical engineering, the appropriate thickness of the FGP-GPLRC core should be selected according to the boundary conditions and other factors, and the ply angle should be adjusted to obtain more stability of vibration.

Multi-layered solid element for seismic analysis of rubber bearings considering stress continuity based on finite particle method

Rubber bearings are crucial components in seismic isolation systems to mitigate the damaging effects of earthquakes on structures. Rubber bearings generally consist of alternate layers of steel and rubber bonded together. Simplified two-point spring models omit this layered construction and have limitations in adaptability and programmability, while refined multiple solid models lead to substantial computational costs. This study presents an effective and efficient approach to simulate rubber bearings by using multi-layered solid element based on the finite particle method (FPM). The traditional “Zigzag” shape function is extended into the 3D situation to reflect the serrated deformation within the layered construction. Based on the simplified assumption of stress continuity, an iterative approach is presented for the deformation gradient to achieve the force continuity between layers in dynamic nonlinear scenarios. The multi-layered solid models for both natural rubber bearings (NRBs) and lead rubber bearings (LRBs) are proposed based on this element. The errors of the hysteresis curves of rubber bearings are below 3.1 % between the numerical results obtained by using the multi-layered solid model and the experimental results. The computational speedup ratio of the proposed multi-layered solid model is verified to be 19 relative to the refined multiple solid model. The proposed method is applied to a base-isolated frame structure to demonstrate its effectiveness in structural seismic analysis.

Semiclassics for the QCD vacuum structure through T2-compactification with the baryon-’t Hooft flux

We study QCD vacuum structure with the topological θ angle using a recently proposed semiclassical approach on ℝ2 × T2 with the ’t Hooft and baryon magnetic fluxes. Under the assumption of adiabatic continuity in this setup, the confining vacuum can be described by the dilute gas of center vortices. With this semiclassical approach, we derive the 2d effective description at small T2 and successfully explain the reasonable theta dependence of the QCD vacuum: in the one-flavor QCD at θ = π, the CP symmetry is spontaneously broken for quark mass above a critical value and restored for a subcritical mass, while the CP symmetry is always spontaneously broken in the multi-flavor QCD at θ = π. From our semiclassical description, we discuss implications to the 4d chiral Lagrangian and propose how the η′ meson should be incorporated in consistent with known global structures: the periodicity of the η′ should be extended from the naive one 2π to 2πN. Additionally, we revisit the phase diagram of Nf = 1 + 1 and Nf = 1 + 1 + 1 QCD on the up and down quark mass plane, confirming and refining the existence of the CP-broken Dashen phase.

Extragradient method with feasible inexact projection to variational inequality problem

The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint set, as in previous versions extragradient method, the proposed methods compute feasible inexact projections on the constraint set using a relative error criterion. The first version of the proposed method provided is a counterpart to the classic form of the extragradient method with constant steps. In order to establish its convergence we need to assume that the operator is pseudo-monotone and Lipschitz continuous, as in the standard approach. For the second version, instead of a fixed step size, the method presented finds a suitable step size in each iteration by performing a line search. Like the classical extragradient method, the proposed method does just two projections into the feasible set in each iteration. A full convergence analysis is provided, with no Lipschitz continuity assumption of the operator defining the variational inequality problem.

Exponentially improved efficient machine learning for quantum many-body states with provable guarantees

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m-dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ, provided that a sample set (of size N) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N=mO(1ɛ), was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n, with N=poly(ɛ−1,n,ln1δ), where poly denotes a polynomial function, and (1−δ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N=poly(ɛ−1,lnnδ). Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024

Non-supersymmetric duality cascade of QCD(BF) via semiclassics on ℝ2× T2 with the baryon-’t Hooft flux

We study the phase diagrams of the bifundamental QCD (QCD(BF)) of different ranks, which is the 4d SU(N1) × SU(N2) gauge theory coupled with a bifundamental Dirac fermion. After discussing the anomaly constraints on possible vacuum structures, we apply a novel semiclassical approach on ℝ2× T2 with the baryon-’t Hooft flux to obtain the concrete dynamics. The 2d effective theory is derived by the dilute gas approximation of center vortices, and it serves as the basis for determining the phase diagram of the model under the assumption of adiabatic continuity. As an application, we justify the non-supersymmetric duality cascade between different QCD(BF), which has been conjectured in the large-N argument. Combined with the semiclassics and the large-N1,2 limit, we construct the explicit duality map from the parent theory, SU(N1) × SU(N2) QCD(BF), to the daughter theory, SU(N1) × SU(N2− N1) QCD(BF), including the correspondence of the coupling constants. We numerically examine the validity of the duality also for finite N1,2 within our semiclassics, finding a remarkable agreement of the phase diagrams between the parent and daughter sides.

About the Subgradient Method for Equilibrium Problems

Convergence results of the subgradient algorithm for equilibrium problems were mainly obtained using a Lipschitz continuity assumption on the given bifunctions. In this paper, we first provide a complexity result for monotone equilibrium problems without assuming Lipschitz continuity. Moreover, we give a convergence result of the value of the averaged sequence of iterates beyond Lipschitz continuity. Next, we derive a rate convergence in terms of the distance to the solution set relying on a growth condition. Applications to convex minimization and min–max problems are also stated. These ideas and results deserve to be developed and further refined.

SL n Contravariant Matrix-Valued Valuations on Polytopes

Abstract Without any continuity assumptions, a complete classification of $\textrm{SL}(n)$ contravariant, matrix-valued valuations on convex polytopes is established. Furthermore, the constraint for matrix symmetry is removed. If $n\geq 4$, then such valuations are uniquely characterized by the generic Lutwak–Yang–Zhang matrix; in dimension three, a new function appears. The classification result in the 2-dimensional case is consistent with the established example of $\textrm{SL}(2)$-equivariant matrix-valued valuation.

QUALITATIVE ANALYSIS ON THE INTERFERENCE AND CAUSALITY BETWEEN ACCOUNTING AND AUDITING FOR ROMANIAN COMPANIES “TOP TRADED” LISTED AT THE BUCHAREST STOCK EXCHANGE

The instability generated by legislative changes, price volatility, difficulties in obtaining and maintaining financial stability are realities that characterize the current economic situation, and the first indications of significant uncertainties regarding the continuity of an entity's activity can be obtained from the financial statements and the audit report, consequently, it becomes essential to assume the responsibilities that administrators and financial auditors have in assessing the adequacy of the going concern principle. The objective of the research is the analysis of how the auditor, by belonging to the Big 4 or Non-Big 4 category, the audit opinion, the number of key audit aspects included in the audit report, confirms the positive or negative implications on the principle of business continuity. The research methodology involved qualitative analysis by manually extracting data from the audit reports issued for the period 2018-2022, for a sample that includes 45 companies "top traded" from Romania listed on the Bucharest Stock Exchange (BSE). Following the analysis, it was found that the assumption of continuity of activity in the preparation of the individual annual financial statements, assumed by the management of the company, is adequate in 78% of the cases for the studied sample.

Improved stiff string torque and drag prediction using a computationally efficient contact algorithm

ABSTRACT Due to the intermittent contact with the wellbore, determining torque and drag for deviated wells is difficult. Most models have ignored drill string stiffness and assumed continual contact to simplify derivation. However, the accuracy of these ‘soft-string’ models is restricted, especially at high dogleg severities. On the other hand, most ‘stiff-string’ models rely on computationally intensive approaches or continuous contact assumptions. To mitigate these issues, a computationally efficient penalty-based wellbore contact algorithm has been developed based on vector calculation, which at most requires two dot products and three arithmetic operations to determine contact locations. This algorithm is incorporated into a 3D multibody dynamics (MBD) model, which utilizes rigid drill-string segments based on the Newton-Euler formulation, connected via axial, shear, torsional, and bending springs to capture drill string flexibility. This model performs simulations faster than real-time and has been validated using surface measurements from a completed well.

An accelerated relaxed-inertial strategy based CGP algorithm with restart technique for constrained nonlinear pseudo-monotone equations to image de-blurring problems

In this paper, an accelerated spectral conjugate gradient projection algorithm is proposed for solving the constrained nonlinear pseudo-monotone equations. We set a restart procedure related to the conjugate parameter in the search direction of the spectral conjugate gradient method. We use an accelerated gradient descent scheme to generate the spectral parameter. Finally, we adopt the relaxed-inertial strategy to accelerated algorithm iteration process. Global convergence is proved under mild conditions without the Lipschitz continuity assumption. Numerical comparisons with other methods show the performances of our algorithm for solving large-scale equations. Our applications are on regularized decentralized logistic regression and image de-blurring problems.