MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early

This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (Vmax), maximum tardy job, denoted by (Tmax), and maximum earliness (Emax). We propose several algorithms based on types of objectives function to be optimized when dealing with simultaneous minimization problems with and without weight and hierarchical minimization problems. The proposed Algorithm (3) is to find the set of efficient solutions for 1//F (Vmax, Tmax, Emax) and 1//(Vmax + Tmax + Emax). The Local Search Heuristic Methods (Descent Method (DM), Simulated Annealing (SA), Genetic Algorithm (GA), and the Tree Type Heuristics Method (TTHM) are applied to solve all suggested problems. Finally, the experimental results of Algorithm (3) are compared with the results of the Branch and Bound (BAB) method for optimal and Pareto optimal solutions for smaller instance sizes and compared to the Local Search Heuristic Methods for large instance sizes. These results ensure the efficiency of Algorithm (3) in a reasonable time.

Optimized model-based control of main mine ventilation air flows with minimized energy consumption

In early 2018,the Boliden Garpenberg operation implemented an optimized control strategy as an addition to the existing ventilation on demand system.The purpose of the strategy is to further minimize energy use for main and booster fans,whilst also fulfilling airflow setpoints without violating constraints such as min/max differential pressure over fans and interaction of air between areas in mines.Using air flow measurements and a dynamical model of the ventilation system,a mine-wide coordination control of fans can be carried out.The numerical model is data driven and derived from historical operational data or step changes experiments.This makes both initial deployment and lifetime model maintenance,as the mine evolves,a comparably easy operation.The control has been proven to operate in a stable manner over long periods without having to re-calibrate the model.Results prove a 40%decrease in energy use for the fans involved and a greater controllability of air flow.Moreover,a 15%decrease of the total air flow into the mine will give additional proportional heating savings during winter periods.All in all,the multivariable controller shows a correlation between production in the mine and the ventilation system performance superior to all of its predecessors.

Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations

Thermoelastic martensitic transformations in shape memory alloys can be modeled on the basis of nonlinear elastic theory.Microstructures of fine phase mixtures are local energy minimizers of the total energy.Using a one-dimensional effective model,we have shown that such microstructures are inhomogeneous solutions of the nonlinear Euler-Lagrange equation and can appear upon loading or unloading to certain critical conditions,the bifurcation conditions.A hybrid numerical method is utilized to calculate the inhomogeneous solutions with a large number of interfaces.The characteristics of the solutions are clarified by three parameters：the number of interfaces,the interface thickness,and the oscillating amplitude.Approximated analytical expressions are obtained for the interface and inhomogeneity energies through the numerical solutions.

REGULARITIES AND SINGULARITIES OF THE ENERGY MINIMIZERS OF THE HEISENBERG GROUP TARGETS

In this paper, the properties of the maps for the Heisenberg group targets are studied. For u e∈W1,α(Ω, Hm), some Poincare type inequalities are proved. For the energy minimizers, the ∈-regularity theorems and the singularity theorems are obtained.

EXISTENCE AND BLOW-UP BEHAVIOR OF CONSTRAINED MINIMIZERS FOR SCHRDINGER-POISSON-SLATER SYSTEM

In this article, we study constrained minimizers of the following variational problem ε（p）：={u∈H1 inf（R3）,｜｜u｜｜22=p} E（u）,ρ〉0,where E（u） is the SchrSdinger-Poisson-Slater （SPS） energy functional E（u）：1/2∫R3｜△u（x）｜2dx-1/4∫R3∫R3u2（y）u2（x）/｜x-y｜dydx-1/p∫R3｜u（x）∫pdx in R3,and p ∈ （2,6）. We prove the existence of minimizers for the cases 2 〈 p 〈10/3, p 〉 0, and P =10/3, 0 〈 p 〈 p＊, and show that e（ρ） = -∞ for the other cases, where p＊ = ｜｜φ｜｜22 and φ（x） is the unique （up to translations） positive radially symmetric solution of -△u ＋ u = u7/3 in R3. Moreover, when e（ρ＊） = -∞, the blow-up behavior of minimizers as p/p＊ is also analyzed rigorously.

A REMARK ON THE REGULARITY OF VECTOR-VALUED MAPPINGS DEPENDING ON TWO VARIABLES WHICH MINIMIZE SPLITTING-TYPE VARIATIONAL INTEGRALS

We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.

Higher-Order Minimizers and Generalized (F,<i>ρ</i>)-Convexity in Nonsmooth Vector Optimization over Cones

In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.

Asymptotics for Radial Minimizers of a Ginzburg-Landau Type Functional

The behavior of radial minimizers for a Ginzburg-Landau type functional is considered. The weak convergence of minimizers in W1,n is improved to the strong convergence in W1,n. Some estimates of the rate of the convergence for the module of minimizers are presented.

Optimal Placement of Reclosers to Minimize Power Losses during Non-Load Bearing Disturbances in a Power Distribution Using Firefly Algorithm

The research reported in this paper focuses on non-technical power loss reduction for power distribution systems. Such reduction of costs of energy not served (ENS.COST), is intelligently evaluated and optimized using a firefly algorithm, from where savings of 43.3% on energy not served are achieved.

On-chip cyclic-AWG-based 12 × 12 silicon wavelength routing switches with minimized port-to-port insertion loss fluctuation

With the rapidly increasing bandwidth requirements of optical communication networks, compact and low-cost large-scale optical switches become necessary. Silicon pbotonics is a promising technology due to its small footprint, cost competitiveness, and high bandwidth density. In this paper, we demonstrate a 12 × 12 silicon wavelength routing switch employing cascaded arrayed waveguide interconnection network on a the switch＇s footprint. We single chip. We optimize develop an algorithm based gratings （AWGs） connected by a silicon waveguide the connecting strategy of the crossing structure to reduce on minimum standard deviation to minimize the port-to- port insertion loss （IL） fluctuation of the switch globally. The simulated port-to-port IL fluctuation decreases by about 3 dB compared with that of the conventional one. The average measured port-to-port IL is 13.03 dB, with a standard deviation of 0.78 dB and a fluctuation of 2.39 dB. The device can be used for wide applications in core networks and data centers.

Conversion of D-glucose to L-lactate via pyruvate by an optimized cell-free enzymatic biosystem containing minimized reactions

Cell-free synthetic enzymatic biosystem is emerging to expand the traditional biotechnological mode by utilizing a number of purified/partially purified enzymes and coenzymes in a single reaction vessel for the production of desired products from low-cost substrates.Here,a cell-free synthetic biosystem containing minimized number of reactions was designed for the conversion of D-glucose to L-lactate via pyruvate.This NADH-balanced biosystem was comprised of only 5 thermophilic enzymes without ATP supplementation.After optimization of enzyme loading amounts,buffer concentration and cofactor concentration,D-glucose was converted to L-lactate with a product yield of∼90%.Our study has provided an emerging platform with potentials in producing pyruvatederived chemicals,and may promote the development of cell-free synthetic enzymatic biosystems for biomanufacturing.

Beyond statistical significance:Embracing minimal clinically important difference for better patient care

The minimal clinically important difference(MCID)represents a pivotal metric in bridging the gap between statistical significance and clinical relevance,addressing the direct impact of medical interventions from the patient's perspective.This comprehensive review analyzes the evolution,applications,and challenges of MCID across medical specialties,emphasizing its necessity in ensuring that clinical outcomes not only demonstrate statistical significance but also offer genuine clinical utility that aligns with patient expectations and needs.We discuss the evolution of MCID since its inception in the 1980s,its current applications across various medical specialties,and the methodologies used in its calculation,highlighting both anchor-based and distribution-based approaches.Furthermore,the paper delves into the challenges associated with the application of MCID,such as methodological variability and the interpretation difficulties that arise in clinical settings.Recommendations for the future include standardizing MCID calculation methods,enhancing patient involvement in setting MCID thresholds,and extending research to incorporate diverse global perspectives.These steps are critical to refining the role of MCID in patient-centered healthcare,addressing existing gaps in methodology and interpretation,and ensuring that medical interventions lead to significant,patient-perceived improvements.

FINDING THE STRICTLY LOCAL AND ε-GLOBAL MINIMIZERS OF CONCAVE MINIMIZATION WITH LINEAR CONSTRAINTS

This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Basing on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an θ-global minimizer of the problem.

An oracle inequality for regularized risk minimizers with strongly mixing observations

We establish a general oracle inequality for regularized risk minimizers with strongly mixing observations, and apply this inequality to support vector machine （SVM） type algorithms. The obtained main results extend the previous known results for independent and identically distributed samples to the case of exponentially strongly mixing observations.

W0^1p（x） Versus C^1 Local Minimizers for a Functional with Critical Growth

Let Ω IR^N, （N ≥ 2） be a bounded smooth domain, p is Holder continuous on Ω^-, 1 〈 p^- ：= inf pΩ（x） ≤ p＋ = supp（x） Ω〈∞, and f：Ω^-× IR be a C^1 function with f（x,s） ≥ 0, V （x,s） ∈Ω × R^＋ and sup ∈Ωf（x,s） ≤ C（1＋s）^q（x）, Vs∈IR^＋,Vx∈Ω for some 0〈q（x） ∈C（Ω^-） satisfying 1 〈p（x） 〈q（x） ≤p^＊ （x） -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^＋ ≤ q- ≤ q＋. As usual, p＊ （x） = Np（x）/N-p（x） if p（x） 〈 N and p^＊ （x） = ∞- if p（x） if p（x） 〉 N. Consider the functional I： W0^1,p（x） （Ω） →IR defined as I（u） def= ∫Ω1/p（x）｜△｜^p（x）dx-∫ΩF（x,u^＋）dx,Vu∈W0^1,p（x）（Ω）,where F （x, u） = ∫0^s f （x,s） ds. Theorem 1.1 proves that if u0 ∈ C^1 （Ω^-） is a local minimum of I in the C1 （Ω^-） ∩C0 （Ω^-）） topology, then it is also a local minimum in W0^1,p（x） （Ω）） topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation （P） defined below.

The graph limit of the minimizer of the Onsager-Machlup functional and its computation

The Onsager-Machlup(OM)functional is well known for characterizing the most probable transition path of a diffusion process with non-vanishing noise.However,it suffers from a notorious issue that the functional is unbounded below when the specified transition time T goes to infinity.This hinders the interpretation of the results obtained by minimizing the OM functional.We provide a new perspective on this issue.Under mild conditions,we show that although the infimum of the OM functional becomes unbounded when T goes to infinity,the sequence of minimizers does contain convergent subsequences on the space of curves.The graph limit of this minimizing subsequence is an extremal of the abbreviated action functional,which is related to the OM functional via the Maupertuis principle with an optimal energy.We further propose an energy-climbing geometric minimization algorithm(EGMA)which identifies the optimal energy and the graph limit of the transition path simultaneously.This algorithm is successfully applied to several typical examples in rare event studies.Some interesting comparisons with the Freidlin-Wentzell action functional are also made.

Torque control strategy with V2X information for HEVs to minimize fuel consumption

Today,much information from traffic infrastructures and sensors of ego vehicle is available.Using such information has a potential for internal combustion engine vehicle to reduce fuel consumption in real world.In this paper,a powertrain controller for a hybrid electric vehicle aiming to reduce fuel consumption is introduced,which uses information from traffic signals,the global positioning system and sensors,and the preceding vehicle.This study was carried out as a benchmark problem of engine and powertrain control simulation and modeling 2021(E-COSM 2021).The developed controller firstly decides reference acceleration of the ego vehicle using the traffic signal and the position information and the preceding vehicle speed.The acceleration and deceleration leading to increase in unnecessary fuel consumption is avoided.Next,the reference engine,generator,and motor torques are decided to achieve the reference acceleration and minimize fuel consumption.In addition,the reference engine,generator and motor torques were decided by the given fuel consumption map for the engine,and by the virtual fuel consumption maps for the generator and the motor.The virtual fuel consumption is derived from the efficiency maps of the generator and the motor using a given equivalent factor,which converts electricity consumption to fuel for the generator and the motor.In this study,a controller was designed through the benchmark problem of E-COSM 2021 for minimizing total fuel consumption of the engine,the generator,and the motor.The developed controller was evaluated in driving simulations.The result shows that operating the powertrain in efficient area is a key factor in reducing total fuel consumption.