Optimal bundles for sponsored search auctions via bracketing scheme

Sponsored search auction has been recently studied and auctioneer's revenue is an important consideration in probabilistic single-item second-price auctions. Some papers have analyzed the revenue maximization problem on different methods to bundle contexts. In this paper, we propose a more flexible and natural method which is called the bracketing method. We prove that finding a bracketing scheme that maximizes the auctioneer's revenue is strongly NP-hard. Then, a heuristic algorithm is given. Experiments on three test cases show that the revenue of the optimal bracketing scheme is very close to the optimal revenue without any bundling constraint, and the heuristic algorithm performs very well. Finally, we consider a simpler model that for each row in the valuation matrix, the non-zero cells have the same value. We prove that the revenue maximization problem with Kanonymous signaling scheme and cardinality constrained signaling scheme in this simpler model are both NP-hard.

Research and Analysis on Anti-corrosion of Mountain Photovoltaic Brackets

With the increasing global demand for renewable energy,solar photovoltaic power generation technology has been widely applied in China and even globally.Especially in mountainous areas,complex terrain resources are cleverly utilized in the construction of photovoltaic power stations,but this also brings severe challenges to the anti-corrosion of photovoltaic brackets.This paper focuses on the anti-corrosion technology of mountain photovoltaic brackets,and deeply explores the influence of natural factors such as mountain climate,sandstorms,and precipitation on the corrosion of photovoltaic brackets.The research results show that the key to improving anti-corrosion performance lies in the selection of bracket materials and optimization of coating processes.After comparing various anti-corrosion treatment methods such as hot-dip galvanizing,spray aluminum coating,and new anti-corrosion materials,it is found that nano coating technology exhibits excellent protective effects in corrosive environments.This study is of great significance for promoting the sustainable development of photovoltaic power generation,providing solid theoretical support and practical guidance for the anti-corrosion design of mountain photovoltaic power stations.

Effect of Dietary Components on the Shear Bond Strength of Orthodontics Brackets after Thermal Aging

Introduction: The stability of orthodontic brackets throughout orthodontic treatment plays a critical role in the treatment’s effectiveness. The present in vitro study was designed to assess the impact of various dietary components on the performance of orthodontic brackets. Methods: Metal orthodontic brackets were bonded to 66 extracted anterior teeth divided into groups based on the solution type: Milk, Gatorade, Cold Coffee, and a control group using water. Each group consisted of 20 teeth except for the control group, which included six teeth. The bracketed teeth were submerged in their respective solutions for 15 minutes three times daily at different intervals to mimic an in vivo environment and were stored in artificial saliva at room temperature (23?C). The specimens underwent artificial aging through 10,000 cycles of thermocycling (representing one clinical year) between 5?C and 55?C. Shade measurements were taken using a VITA Easy Shade device, capturing the classic shade and L*, a*, and b* values. Delta E values were calculated immediately post-bonding and after 7 days, 1 month, 1, and 2 clinical years. The shear bond strength of each bracket was measured using an ultra-tester machine. Results: After two clinical years, significant differences in ΔE color values were observed across all groups, with the most substantial change noted in teeth immersed in cold coffee. Brackets submerged in milk demonstrated lower shear bond strength than other solutions, whereas the control group exhibited the highest shear bond strength (P = 0.01). Conclusion: The study indicates that dietary components significantly influence tooth color stability and the shear bond strength of orthodontic brackets, underscoring the importance of considering these factors in orthodontic treatment planning.

Application Strategies of the Bracket Set in Modern Architectural Design

The Bracket Set(dougong)is an important aspect of traditional Chinese architecture known for its exquisite structure,complexity,and rich variations.This design element has been used since the Qin and Han Dynasties and is still prevalent today.It highlights hierarchy and spiritual connotations in the design of a building.This article explores the application of Bracket Set elements in modern architectural design.It analyzes the specific application strategies of this design element,highlighting its value in modern architecture.The goal is to provide modern architectural designers with multiple perspectives and strategies to fully utilize the advantages of Bracket Set elements in architectural design and enhance the artistic value of their work.

High-Order Iterative Methods Repeating Roots a Constructive Recapitulation

This paper considers practical, high-order methods for the iterative location of the roots of nonlinear equations, one at a time. Special attention is being paid to algorithms also applicable to multiple roots of initially known and unknown multiplicity. Efficient methods are presented in this note for the evaluation of the multiplicity index of the root being sought. Also reviewed here are super-linear and super-cubic methods that converge contrarily or alternatingly, enabling us, not only to approach the root briskly and confidently but also to actually bound and bracket it as we progress.

BracKet间接粘着法的临床应用

目的:提高固定矫治器中BracKet的粘接精度,使矫治器发挥最佳矫治疗效。方法:先将BracKet精确地粘接在石膏模型上,后用0.5 mm胶模制做转移模托,将BracKet再转移到模托上。最终将BracKet精确地粘着于牙面上。结果:通过临床观察证明BracKet间接粘着法克服了直接粘着法中BracKet位置不准确,BracKet的粘接高度和角度不易控制的缺点,能使BracKet精确地粘与牙面。结论:随着固定矫治器的不断发展,临床上对BracKet的粘着精度越来越高,为了达到此目标,提高矫治疗效,采用BracKet间接粘着法将托槽的粘着精度大大提高。

Research on semi-solid thixoforming process of AZ91D magnesium alloy brackets for generators in JH70-type motorbikes

The investment on semi-solid die casting processes of AZ91D magnesium alloy brackets for generators in JH70-type motorbikes is introduced. The processes of low super-heat and cooling slope for the preparation of billets with non-dendritic microstructure, the remelting of billets for thixoforming and the parameters in the process of semi-sohd thixoforming have been researched. The results show that primary billets with non-dendritical structures can be prepared by forming great amount of nuclei in melt via the process of low super heat. By optimizing the remelting process through adjusting the current of the induced equipment, semi-solid billets with a structure of spherical grains were obtained from the primary billets with non-dendritical structure. The range of 580℃ to 583℃ is the proper remelting temperatures by which the billets have an expected thixotropy and can be transferred to a die-casting machine. The optimized parameters of semi-solid forming in a die-casting machine are as follows： the area of the ingate in the die is 383.5 mm^2, the speed of the pierce of the machine 5 m/s, the shot pressure of the pierce 75 MPa, and the maintenance pressure of the pierce 350 MPa. The castings of brackets for supporting generators in JH70 type motorbikes were formed by adopting the optimized processes and parameters mentioned above.

Numerical simulation and optimization of shell mould casting process for leaf spring bracket

Although the shell mould casting process has a wide range of application in many fields,the prediction of casting defects is still a problem.In the present work,a typical leaf spring bracket casting of ZG310-570 was fabricated by shell mold casting.The finite element model and ProCAST software were utilized for simulating the filling and solidification processes of the casting;and the formation mechanism of the gas pore,and shrinkage porosity defects were analyzed.The results indicate that the gas pore and shrinkage porosity defects are formed due to air entrapment,insufficient feeding and non-sequential solidification.Subsequently,through changing the position of risers,adding a connecting channel between the risers,and setting blind risers at the U-shaped brackets,an optimized gating and feeding system was established to improve the quality of the casting.After optimization,the gas pore and shrinkage porosity defects of the leaf spring bracket casting are effectively eliminated.The experiment results with the optimized casting process are in good agreement with the numerical simulation,which verifies the validity of the finite element model in the shell mould casting.

HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane.

Structural Stress Monitoring and FEM Analysis of the Cutting Operation of the Main Bracket of A Semi-Submersible Platform

For a semi-submersible platform in repair, the eight old main brackets which connect columns with pontoons need to be replaced by new ones. In order to ensure the safety of the cutting operation of the old main bracket and calculate the initial stress condition of new main bracket, the structural stress monitoring of eight key spots is carried out, and then the calibrated finite element model is established according to the field monitoring results. Before cutting the main bracket and all associated structures, eight rectangular rosettes were installed, and a tailored cutting scheme was proposed to release the initial stress, in which the main bracket and associated column and pontoon plates were partly cut. During the cutting procedure, the strains of the monitoring spots were measured, and then the structural stress of the monitored spots were obtained. The stress variation characteristics at different spots during the initial cutting operation were shown and the initial stress condition of the monitored spots was figured out. The loading and support conditions of the semi-submersible platform were calibrated based on the measured initial stress condition, which made the finite element model more credible. The stress condition with the main bracket and associated structures being entirely cut out is analyzed by the Finite Element Method (FEM), which demonstrates the cutting operation to be safe and feasible. In addition, the calibrated finite element model can be used to calculate the initial stress condition of the new main bracket, which will be very helpful for the long-term stress monitoring on the main bracket.

Generalized Toda Mechanics Associated with Classical Lie Algebras and Their Reductions

For any classical Lie algebra , we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers . The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson brackets are provided, and explicit examples for with are also given. For all , it is shown that the dynamics of the - and the -Toda chains are natural reductions of that of the -chain, and for , there is also a family of symmetrically reduced Toda systems, the -Toda systems, which are also integrable. In the quantum case, all -Toda systems with 1$' SRC='http://ej.iop.org/images/0253-6102/41/3/339/ctp_41_3_339_12.gif'/> or 1$' SRC='http://ej.iop.org/images/0253-6102/41/3/339/ctp_41_3_339_13.gif'/> describe the dynamics of standard Toda variables coupled to noncommutative variables. Except for the symmetrically reduced cases, the integrability for all -Toda systems survive after quantization.

An Integrating Algorithm and Theoretical Analysis for Fully Rheonomous Affine Constraints: Completely Integrable Case

This paper develops an integrating algorithm for fully rheonomous affine constraints and gives theoretical analysis of the algorithm for the completely integrable case. First, some preliminaries on the fully rheonomous affine constraints are shown. Next, an integrating algorithm that calculates independent first integrals is derived. In addition, the existence of an inverse function utilized in the algorithm is investigated. Then, an example is shown in order to evaluate the effectiveness of the proposed method. By using the proposed integrating algorithm, we can easily calculate independent first integrals for given constraints, and hence it can be utilized for various research fields.

Inverse Transformation of Elliptical Relative State Transition Matrix

A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.

Clinical assessment of demineralization and remineralization surrounding orthodontic brackets with FluoreCam

Objective: To determine quantitatively the amount of demineralization and the ability of commercially available products and an experimental cream to inhibit or reverse orthodontic related demineralization.Methods: A total of 20 patients who were 25–35 years old and having orthodontic treatment for 6–8 months were chosen.Caries risk assessments were done for each patient and ones with "moderate risk" were included.Patients with fixed orthodontic appliances were divided into 4 groups(5 patients each) including one control and 3 study groups.All patients used same toothpaste 2 times a day during the 3 weeks study period.Additional to the toothpaste first study group used MI Paste Plus(GC, Tokyo, Japan), second study group used Remin Pro(Voco, Cuxhaven, Germany) and third group used an experimental remineralizing cream per day for 3 weeks.Maxillary central and lateral incisors of each patient were examined by FluoreCam(Daraza Therametric Technologies, USA) device.The examinations were performed at baseline and at the end of 1st, 2nd and 3rd weeks.Results: According to the FluoreCam measurements the control group showed significant amount of demineralization at the end of 3 weeks, moreover the amount of demineralization has gradually increased in time.At the end of the study all 3 study groups showed significant amount of remineralization and the amount of remineralization for all the 3 study groups has gradually increased in time.However the amount of remineralization for 3rd study group was lesser than the 1st and 2nd study groups.The remineralization amounts for the 1st and 2 nd study groups were determined to be identical.Conclusions: This study demonstrated that demineralization is measurable around orthodontic brackets and the demineralization can be completely inhibited and/or reversed by the use of commercially available remineralization products.

The Evaluation of a Resin-modified Glass Ionome Cement for Bonding Orthodontic Brackets

To evaluate the shear bond strength（SBS） and bond failure interface after the debonding of orthodontic brackets with a resin-modified glass ionomer cement（RMGIC） under six bonding conditions, 140 premolar teeth were randomly divided into seven groups. The brackets of all groups, except for control group, were bonded using a RMGIC. The teeth were debonded using a universal testing machine. The shear bond strength, adhesive remnant index （ARI） and enamel fracture were examined for each debonding. A significant difference existed in SBS under wet and dry conditions in two groups of Fuji Ortho LC. Different degree of enamel fracture was seen in groups of Fuji Ortho LC（dry/37% phosphoric acid treated） after debonding. Bond failed predominantly at the enamel-adhesive interface, except for phosphoric acid treated groups. The RMGIC achieve a clinically effective adhesion in orthodontics under different bonding conditions.

r-Matrix Structure for a Restricted Flow with Bargmann Constraint

This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure.

Generalized Toda Mechanics Associated with Loop Algebras L（Cr） and L（Dr） and Their Reductions

We construct a class of integrable generalization of Toda mechanics withlong-range interactions. These systems are associated with the loop algebras L(C_r) and L(D_r) inthe sense that their Lax matrices can he realized in terms of the c = 0 representations of theaffine Lie algebras C_r~((1)) and D_r~((1)) and the interactions pattern involved bears the typicalcharacters of the corresponding root systems. We present the equations of motion and the Hamiltoninnstructure. These generalized systems can be identified unambiguously by specifying the underlyingloop algebra together with an ordered pair of integers (n, m). It turns out that different systemsassociated with the same underlying loop algebra but with different pairs of integers (n_1, m_1) and(n_2, m_2) with n_2 【 n_1 and m_2 【 m_2 can be related by a nested Hamiltonian reduction procedure.For all nontrivial generalizations, the extra coordinates besides the standard Toda variables arePoisson non-commute, and when either n or m ≥ 3, the Poisson structure for the extra coordinatevariables becomes some Lie algebra (i.e. the extra variables appear linearly on the right-hand sideof the Poisson brackets). In the quantum case, such generalizations will become systems withnoncommutative variables without spoiling the integrability.

Development of micro wire electrical discharge machining platform and its application

A machining platform of micro wire electrical discharge machining (MWEDM) was developed. The key technology of MWEDM mainly includes granite basement, micro energy pulse generator, detection and servo control system, constant tension winding system and V-block guide wire mechanism. Utilizing micro wire electrode with 30μm in diameter, the MWEDM can machine the micro slot with the minimum size of 38μm wide, and the surface roughness is smaller than 0.1μm, the machining precision is less than 0.5μm, the white layer is no more than 2μm with main cut. All kinds of complex micro parts, such as micro gear, micro bearing bracket and micro shaped holes, can also be machined by using this platform.

Symplectic-like Difference Schemes for Generalized Hamiltonian Systems

The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.

Generalized Toda Mechanics Associated with Loop Algebra L（Br）

A class of generalization of Toda mechanics with long range interactions isconstructed in this paper. These systems are associated with the loop algebras L(B_r) in the sensethat their Lax matrices can be realized in terms of the c = 0 representations of the affine Liealgebras B_r~((1)) . We adopt a pair of ordered integers (m, n) to describe the Toda mechanicssystem when we present the equations of motion and the Hamiltonian structure. We also extract theclassical r matrix which satisfy the classical Yang-Baxter relation. Such generalizations willbecome systems with noncommutative variables in the quantum case.