Study of Fixed Point Theorems for Higher Dimension in Partially Ordered Metric Spaces

In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our work. Our results generalize the recent fixed point theorems cited in [1]-[4] etc. and include several recent developments.

The Effect of Non-Contact Conditions in a Splinted Fixed Partial Denture on the Load Sharing Mechanism： A Finite Element Study

A computer-aided design model for a fixed partial denture was constructed and used in a finite element analysis to study the overall load sharing mechanism between the fixed partial denture and oral structures while the denture base rested on the al- veolar ridge. To investigate the consequences of non-contact conditions, three additional models were generated incorporating a uniform clearance of 0.125 mm, 0.25 mm, and 0.5 mm, respectively. A 100 N static load located at the free end of the prosthesis was applied while the distal portion of the jaw was set fixed. The results show that whilst releasing the ridge almost entirely, the presence of the clearance drastically increased the load on the splinting teeth. A pull-out force on the canine tooth of about 44 N was computed, accompanied by a mesio-distal moment of about 500 N.cm. The combination of which was similar to the tooth extraction maneuver performed by the dentist. In contrast, the second premolar was found to bear a push-in force of almost 115 N. The first molar, though barely solicited in the contact condition, became substantially loaded in non-contact conditions, which validates the choice of sacrificing three teeth to support the denture.

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized （ψ, Ф）-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.

Effect of Accessory Retention Forms on the Bond Strength of Resin-bonded Fixed Partial Dentures:a 3D Finite Element Study

Interface debonding between prostheses and abutments was the most frequent failure mode of resin-bonded fixed partials dentures(RBFPDs) in clinic. The purpose of this study was to investigate the effect of accessory retention forms on the bond strength of RBFPDs. Three types of 3D finite element models were constructed.The model of posterior metal plate RBFPD with spoon-shaped occlusal rest seats served as the control. The remaining two types of models based on the control added the retention form design of the pin hole and axial groove respectively. The axial or buccolingual load of 150 N was applied on the prosthesis, first premolar and first molar respectively. The maximum principal stresses of the adhesive layer in different models were calculated. Under the load of the same magnitude, the stress due to the buccolingual load was significantly higher than that due to the axial load in the adhesive layer. The proximal shoulder, occlusal rest seats wall and the proximal margin adjacent to the shoulder were the high risk region where the adhesive layer damaged easily. Compared with the control model, the pin and groove models could slightly decrease the stress in the adhesive layer after the axial loading, while the stress in the adhesive layer drastically decreased after horizontal loading and reduced by 22% and 31% respectively. These results indicate that the horizontal occlusal force has a more serious harm to the debonding of RBFPDs. In addition, the accessory retention forms(e.g. pin and axial groove retention forms) can decrease the stress level in the adhesive layer, which are conducive to increase the load-bearing capacity of RBFPDs.

Clinical performance of removable partial dentures: A retrospective clinical study

Removable partial dentures (RPDs) (conventional and implant-supported) treatment is considered a viable option to replace missing teeth as inexpensively as possible, but it has limitations. Objectives: This study reports the effect of gender and location (maxilla vs. mandible) on the clinical performance of removable partial dentures (RPDs). Materials and Methods: A total of 100 Patients who had RPDs delivered between 1990-1995 were evaluated. A 4-point scoring system was used to assess seventeen criteria. These criteria include acceptance, stability, support, retention, adaptation, occlusion, integrity, and design of the pros-theses, rest and rest seat preparation, occlusal wear, esthetics, phonetics, tissue condition, mobility of abutments, gingival and plaque indices. The data were analyzed using Kruskal-Wallis and Mann-Whitney U non-parametric statistical tests. Results: The results showed that acceptance of RPDs was rated the lowest. Other reasons for failure were poor retention, lack of integrity of the prostheses and inadequate adaptation. Retention and design of major connectors attributed to Mandibular RPD failure. Success rate of 75% was observed in male compared with 67.2% for female. Maxillary RPDs showed a higher success rate (78%) compared with the mandibular (70.1%). No significant statistical difference in Alpha scores between female and male patients and between maxillary and mandibular RPDs (p < 0.05). Conclusions: The clinical performance of RPDs showed a higher success rate in male patients compared to female patients and the maxillary RPDs showed a higher success rate compared to mandibular.

The Effect of Partial Removable Denture Use on Oral Health Related Quality of Life and Masticatory Function, after 5 Years Use

The aim of this study was to evaluate whether partial removable denture use indeed leads to improved oral health related quality of life and masticatory function. Materials and Methods: Partially edentulous patients presenting for removable denture treatment at the Prosthodontics Service in the Hospital Affiliated to Kinshasa University (Democratic Republic of Congo) were assessed for enrolment in this study. After applying exclusion criteria, 378 patients were included in the study, and randomly assigned into 2 groups. Oral health related quality of life (OHIP-23) and mastication time (MaT), number of chewing cycles (MaC), mastication frequency (MaF), and the sizes of the peanut fragments (FraS) were compared in both groups. Statistical significance was set at p < 0.05. Results: The average MaC, MaT, MaF, and FraS were 119 (± SD 53.70), 86.75 (±SD 35.35), 1.38 (±SD 0.25), and 3.3 (±SD 3.25) for the denture group and 77.9 (±SD 23.9), 60.2 (±SD 17.91), 1.29 (±SD 0.15), and 1.5 (±SD 0.7) for the non-denture group, respectively. Conclusion: The overall oral health related quality of life was best in the non-denture than denture.

Risks Factors of Caries and Periodontal Diseases in the Patients, after 5 Years Use a Partial Removable Denture

Objective: The goal of the removable partial denture is to restore impaired esthetics and masticatory function by replacing missing teeth. The aim of this study was to establish a possible correla-tion between removable partial denture in acrylic resin use after 5 years and dental diseases. Materials and Methods: Partially edentulous patients presenting for removable denture treatment at the Prosthodontics service of the Affiliated Hospital of Kinshasa University, Democratic Republic of Congo were assessed in this study. Patients were randomly assigned into 2 groups: Denture and non-denture group. Caries and periodontal diseases were compared between both groups. Statistical significance was set at p < 0.05. Results: The average age in the denture and non-denture-group was 53.15 (±SD 22.05) and 31.59 (±SD 11.98) years. Out of 160 teeth were decayed, both 110 teeth (68.75%) in the denture-group and 50 teeth (31.25%) in the non-denture group. The DMFT index calculated at start time of the study was 0.2 for both groups, after five years was 7.1 for the denture-group and 2.6 for the non-denture-group. The plaque index in the denture-group had an index of 1 and that of non-denture-group was 0.5. Conclusion: The relationship has been found between patients’ wearers a RPD and dental diseases.

Common Fixed Point Result of Multivalued and Singlevalued Mappings in Partially Ordered Metric Space

In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.

<i>N</i>-Order Fixed Point Theory for N-Order Generalized Meir-Keeler Type Contraction in Partially Ordered Metric Spaces

This paper concerns N-order fixed point theory in partially ordered metric spaces. For the sake of simplicity, we start our investigations with the tripled case. We define tripled generalized Meir-Keeler type contraction which extends the definition of [Bessem Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010), 4508-4517]. We then discuss the existence and uniqueness of tripled fixed point theorems in partially ordered metric spaces. For general cases, we generalized our results to the N-order case. The results will promote the study of N-order fixed point theory.

Some new fixed point results under constraint inequalities in comparable complete partially ordered Menger PM-spaces

In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger PM-space.We obtain some new results which generalize many known ones in the literature.Moreover,we derive some consequent results and give an example to illustrate our main result.

The Safe Navigation of Partial Motion Planning Based on “Cooperation” with Roadside Fixed Sensors in VANET

In recent years, many methods of safe vehicle navigation and partial motion planning (PMP) have been proposed in vehicular ad-hoc network (VANET) field. In order to improve the limitation of traditional PMP, this paper presents a novel effective way to plan motion with cooperation of roadside fixed sensors (RFSs). With their cooperation, the vehicles can get the surrounding information quickly and effectively, and give highly accurate projections about the near future conditions on road. After proposing our algorithm, the worst case is analyzed and methods are found to solve the problem. Finally we conduct one elemental contrast experiment, driver situation awareness, with or without the “cooperation” of RFSs in highway scenarios. The result shows that the vehicles can make a better PMP based on the forward conditions received from RFSs, and extend the warning distance obviously when emergency happens.

Effect of proximal contact strength on the three-dimensional displacements of implant-supported cantilever fixed partial dentures under axial loading

Objective:This study investigated the effect of proximal contact strength on the three-dimensional displacements of cantilever fixed partial denture(CFPD) under vertically concentrated loading with digital laser speckle(DLS) technique.Methods:Fresh mandible of beagle dog was used to establish the implant-supported CFPD for specimen.DLS technique was employed for measuring the three-dimensional displacement of the prosthesis under vertically concentrated loading ranging from 200 to 3 000 g.The effect of the contact tightness on the displacement of CFPD was investigated by means of changing the contact tightness.Results:When an axial concentrated loading was exerted on the pontic of the implant-supported CFPD,the displacement of the CFPD was the greatest.The displacement of the prosthesis decreased with the increase of contact strength.When the contact strength was 0,0.95,and 3.25 N,the displacement of the buccolingual direction was smaller than that of the mesiodistal direction but greater than that of the occlusogingival direction.When the force on the contact area was 6.50 N,the mesiodistal displacement of the prosthesis was the biggest while the buccolingual displacement was the smallest.Conclusions:The implant supported CFPD is an effective therapy for fully or partially edentulous patients.The restoration of the contact area and the selection of the appropriate contact strength can reduce the displacement of the CFPD,and get a better stress distribution.The most appropriate force value is 3.25 N in this study.

Fixed Point of Multivalued Operators on Partial Metric Spaces

In this paper, we prove some results on fixed point of multivalued operators on partial metric spaces.

Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered <i>G</i>-Partial Metric Spaces

We introduce the concept of generalized quasi-contraction mappings in G-partial metric spaces and prove some fixed point results in ordered G-partial metric spaces. The results generalize and extend some recent results in literature.

A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES

Recently, Suzuki [T. Suzuki characterizes metric completeness, Proc. A generalized Banach contractlon principle that Amer. Math. Soc. 136 （2008）, 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char- acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki＇s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 （2012）, 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric O- completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.

COUPLED FIXED POINTS OF SKEW INCREASINGOPERATORS AND APPLICATIONS

In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.

The extraction of survey lines on partial edentulous models

Survey lines are important features on the dental meshes for removable partial denture frameworks design, but few researche has been done by surveying digital models. This article describes a method for identifying survey line on dental meshes and displays survey line in real time. At the beginning, we segment tooth based on morphologic operators to get the tooth parts. The second step is to calculate the viewing direction perpendicular to the occlusal plane. Finally, we extract boundary points on 2D plane, thereby obtaining a survey line in the surveying direction. We have developed a module to demonstrate survey line in real time.

Common Fixed Point Results for Quasi-contractions Involving Altering Distance Functions in Ordered Cone Metric Spaces

Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.

MEIR-KEELER TYPE CONTRACTIONS FOR TRIPLED FIXED POINTS

In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction：

Endpoints of Multi-Valued Weak Contractions on the Metric Space of Partially Ordered Groups

The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).