SEPARABLE CONDITIONS AND SCALARIZATION OF BENSON PROPER EFFICIENCY

Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.

A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone

We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.

TypeⅠcritical dynamical scalarization and descalarization in Einstein-Maxwell-scalar theory

We investigated the critical dynamical scalarization and descalarization of black holes within the framework of the EinsteinMaxwell-scalar theory featuring higher-order coupling functions.Both the critical scalarization and descalarization displayed first-order phase transitions.When examining the nonlinear dynamics near the threshold,we always observed critical solutions that are linearly unstable static scalarized black holes.The critical dynamical scalarization and descalarization share certain similarities with the typeⅠcritical gravitational collapse.However,their initial configurations,critical solutions,and final outcomes differ significantly.To provide further insights into the dynamical results,we conducted a comparative analysis involving static solutions and perturbative analysis.

Traffic network equilibrium problems with demands uncertainty and capacity constraints of arcs by scalarization approaches

This paper focuses on the vector traffic network equilibrium problem with demands uncertainty and capacity constraints of arcs, in which, the demands are not exactly known and assumed as a discrete set that contains finite scenarios. For different scenario, the demand may be changed, which seems much more reasonable in practical programming. By using the linear scalarization method,we introduce several definitions of parametric equilibrium flows and reveal their mutual relations. Meanwhile, the relationships between the scalar variational inequality as well as the(weak) vector equilibrium flows are explored, meanwhile, some necessary and sufficient conditions that ensure the(weak) vector equilibrium flows are also considered. Additionally, by means of nonlinear scalarization functionals, two kinds of equilibrium principles are derived. All of the derived conclusions contain the demands uncertainty and capacity constraints of arcs, thus the results proposed in this paper improved some existing works. Finally, some numerical examples are employed to show the merits of the improved conclusions.

Critical scalarization and descalarization of black holes in a generalized scalar-tensor theory

We study the critical dynamics in scalarization and descalarization in the fully nonlinear dynamical evolution in the class of theories with a scalar field coupling with both Gauss-Bonnet(GB) invariant and Ricci scalar. We explore the manner in which the GB term triggers black hole(BH) scalarization. A typical type Ⅰ critical phenomenon is observed, in which an unstable critical solution emerges at the threshold and acts as an attractor in the dynamical scalarization. For the descalarization, we reveal that a marginally stable attractor exists at the threshold of the first-order phase transition in shedding off BH hair. This is a new type Ⅰ critical phenomenon in the BH phase transition. Implications of these findings are discussed from the perspective of thermodynamic properties and perturbations for static solutions. We examine the effect of scalar-Ricci coupling on the hyperbolicity in the fully nonlinear evolution and observe that such coupling can suppress the elliptic region and enlarge parameter space in computations.

Scalarizations for Approximate Quasi Efficient Solutions in Multiobjective Optimization Problems

In this paper,by reviewing two standard scalarization techniques,a new necessary and sufficient condition for characterizing(ε,.ε)-quasi(weakly)efficient solutions of multiobjective optimization problems is presented.The proposed procedure for the computation of(ε,.ε)-quasi efficient solutions is given.Note that all of the provided results are established without any convexity assumptions on the problem under consideration.And our results extend several corresponding results in multiobjective optimization.

Conic Scalarizations for Approximate Efficient Solutions in Nonconvex Vector Optimization Problems

Nonlinear scalarization is a very important method to deal with the vector optimization problems.In this paper,some conic nonlinear scalarization characterizations of E-optimal points,weakly E-optimal points,and E-Benson properly efficient points proposed via improvement sets are established by a new scalarization function,respectively.These results improved and generalized some previously known results.As a special case,the scalarization of Benson properly efficient points is also given.Some examples are given to illustrate the main results.

Continuity of Solutions for Parametric Set Optimization Problems via Scalarization Methods

The aim of this paper is to investigate the continuity of solution mappings for para-metric set optimization problems with upper and lower set less order relations by scalarization methods.First,we recall some linear and nonlinear scalarization prop-erties used to characterize the set order relations.Subsequently,we introduce new monotonicity concepts of the set-valued mapping by linear and nonlinear scalarization methods.Finally,we obtain the semicontinuity and closedness of solution mappings for parametric set optimization problems(both convex and nonconvex cases)under the monotonicity assumption and other suitable conditions.The results achieved do not impose the continuity of the set-valued objective mapping,which are obviously different from the related ones in the literature.

Dynamical spontaneous scalarization in Einstein-Maxwell-scalar theory

We study the linear instability and nonlinear dynamical evolution of the Reissner-Nordstrom(RN)black hole in the Einstein-Maxwell-scalar theory in asymptotic flat spacetime.We focus on the coupling function f(φ)=e^(-bφ^(2)),which facilitates both scalar-free RN and scalarized black hole solutions.We first present the evolution of system parameters during dynamic scalarization.For parameter regions in which spontaneous scalarization occurs,we observe that the evolution of the scalar field at the horizon is dominated by the fundamental unstable mode from linear analysis at early times.At late times,the nonlinear evolution can be considered to be the perturbation of scalarized black holes.

SUPER EFFICIENCY AND ITS SCALARIZATION IN TOPOLOGICAL VECTOR SPACE

In this paper, we give a characterization of super efficiency, and obtain a scalarization result for super efficiency in locally convex locally bounded topological vector spaces. The proof given here is substantially different from that given by Borwein and Zhuang.

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

Helmholtz decomposition with a scalar Poisson equation in elastic anisotropic media

P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation can also be used to better understand and distinguish wave types in complex media.At present,the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering,low-rank approximation,and vector Poisson equation.Most of these methods require multiple Fourier transforms or the calculation of large matrices,which require high computational costs for problems with large scale.In this paper,an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain.For 2D problems,the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation.Therefore,compared with existing methods based on pseudoHelmholtz decomposition operators,this method can significantly reduce the computational cost.Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.

High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

The Aharonov-Bohm Effect: An Exploration of Quantum Interference and Electromagnetic Potentials

The AB(Aharonov-Bohm)effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle’s wave function,even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect,an electron beam is split into two paths,with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams,the vector potential A associated with the magnetic flux Φ through the solenoid induces a phase shift in the electron’s wave function.This phase shift,quantified by △φ=qΦ/hc,manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED(quantum electrodynamics),where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems,beyond its classical role.This article outlines the AB effect,including its theoretical framework,experimental observations,and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.

On Scalar Planck Waves

The sound of space-time at the large scale is observed in the form of gravitational waves, which are disturbances in space-time produced by wavelike distortions (or kinks) in the gravitational field of an accelerating parcel or distribution of energy. In this study, we investigate a hypothetical wave mode of quantum space-time, which suggests the existence of scalar Planck waves. According to this hypothesis, the sound of quantum space-time corresponds to kinks propagating in the gravitational displacement field of an oscillating energy density. In evaluating the emission of scalar Planck waves and their effect on the geometry of space-time, one finds that they not only transport a vanishingly small amount of energy but can also be used to simulate gravity.

Structure of Massive “Standard Model” Particles

The massive vector bosons Z o, W ± and the scalar Higgs-boson H o assumed in weak interaction theory, but also the six quarks required in strong interactions are well understood in an alternative quantum field theory of fermions and bosons: Z o and W ± as well as all quark-antiquark states (here only the tt¯state is discussed) are described by bound states with scalar coupling between their massless constituents and have a structure similar to leptons. However, the scalar Higgs-boson H o corresponds to a state with vector coupling between the elementary constituents. Similar scalar states are expected also in the mass region of the mesons ω (0.782 GeV) - Υ ( 9.46 GeV). The underlying calculations can be run on line using the Web-address https://h2909473.stratoserver.net.

Numerical Modeling of Mass Transfer in the Interaction between River Biofilm and a Turbulent Boundary Layer

In this article dedicated to the modeling of vertical mass transfers between the biofilm and the bulk flow, we have, in the first instance, presented the methodology used, followed by the presentation of various results obtained through analyses conducted on velocity fields, different fluxes, and overall transfer coefficients. Due to numerical constraints (resolution of relevant spatial scales), we have restricted the analysis to low Schmidt numbers (Sc=0.1, Sc=1, and Sc=10) and a single roughness Reynolds number (Re*=150). The analysis of instantaneous concentration fields from various simulations revealed logarithmic concentration profiles above the canopy. In this zone, the concentration is relatively homogeneous for longer times. The analysis of results also showed that the contribution of molecular diffusion to the total flux depends on the Schmidt number. This contribution is negligible for Schmidt numbers Sc≥0.1, but nearly balances the turbulent flux for Sc=0.1. In the canopy, the local Sherwood number, given by the ratio of the total flux (within or above the canopy) to the molecular diffusion flux at the wall, also depends on the Schmidt number and varies significantly between the canopy and the region above. The exchange velocity, a purely hydrodynamic parameter, is independent of the Schmidt number and is on the order of 10% of in the present case. This study also reveals that nutrient absorption by organisms near the wall depends on the Schmidt number. Such absorption is facilitated by lower Schmidt numbers.

Convergence,Scalarization and Continuity of Minimal Solutions in Set Optimization

The paper deals with the study of two different aspects of stability in the given space as well as the image space,where the solution concepts are based on a partial order relation on the family of bounded subsets of a real normed linear space.The first aspect of stability deals with the topological set convergence of families of solution sets of perturbed problems in the image space and Painlevé–Kuratowski set convergence of solution sets of the perturbed problems in the given space.The convergence in the given space is also established in terms of solution sets of scalarized perturbed problems.The second aspect of stability deals with semicontinuity of the solution set maps of parametric perturbed problems in both the spaces.

Dynamic of Scalar Bosons in Aharonov-Bohm Magnetic Field

We study the dynamic of scalar bosons in the presence of Aharonov-Bohm magnetic field. First, we give the differential equation that governs this dynamic. Secondly, we use variational techniques to show that the following Schrödinger-Newton equation: , where A is an Aharonov-Bohm magnetic potential, has a unique ground-state solution.