IntroductionLet S and T be two self mappings of a metric space (X, d) Sessa [2] defines S and T to be weakly commuting if d (STx, TSx) < d(Tx, Sx) for all x in X Jungck [1] defines S and T to be compatible if limn_>00(5Txn,T5xn) = 0 whenever {xn} is a sequence in X such that limn_njo Sxn = lim^oo Txn = x for some x in X. By Lemma 1, we suppose that X contains at least three points. LEMMA 2 [1]. Let f and g be compatible self mappings on a metric space (X,d). If f{t) = g(t), then fg(t) = gf(t).The purpose of this paper is to prove some fixed point theorems for compatible mappings satisfying an implicit relation. Implicit relationsLet T be the set of all real continuous functions (.F a ): F(u, v, v,u,u + v, 0 F(u, v, u, v, (Fb): Let be u > 0 and F (u,viu,v,0,u+ vCzhU, where Ci > 0, C2, C3 > 0, ci + 2c2 < 1, and Ci + C3 < 1. F\\ Obviously.(Fa): Let be u > 0 and F (u, v, v,u,u + v (FB) Let be u > 0 and F (u, v,u, v,0,u+v (F0); Let be u > 0 and F (u,v,v,u,u + vwhere hi = f±| < 1.(Fb): Let be u > 0 and F(u, v, u, v,0,u + v F X : Obviously.

In recent years, the IoT concept is more and more powerful, having set the goal of integrating billions of devices to the Internet. Thus, from this perspective, the interest allocated to low-power wireless networks of sensors is higher than ever. In this paper, the SigFox scalability is analyzed from the IoT concept point of view. In the scientific research, there are a series of papers which tackle the SigFox issues, oftentimes at a comparative study level, without evaluating the performance level of the communication protocol. This paper comes to fill this gap by creating a realistic SigFox communication model. Moreover, a developed and tested generator of SigFox traffic has been implemented, using SDRs. This allows the possibility of evaluating the performance level of WSN networks, of a large-scale high-density-type. Both of the suggested instruments represent the novelty of this paper. The obtained results show that the maximum number of sensors that can transmit data at the same time, using the proposed scenarios, is of approximately 100, in order to obtain a high level of performance when the number of available channels is 360. If we are to increase the number of sensors, an avalanche effect ensues which triggers the sharp decrease of the performance of the SigFox network. At the end of this work, a series of solutions are being suggested with the main purpose of increasing the performance level of large-scale, high-density SigFox networks.

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Keratoconus (KTC) is a noninflammatory disorder characterized by progressive thinning, corneal deformation, and scarring of the cornea. The pathological mechanisms of this condition have been investigated for a long time. In recent years, this disease has come to the attention of many research centers because the number of people diagnosed with keratoconus is on the rise. In this context, solutions that facilitate both the diagnostic and treatment options are quickly needed. The main contribution of this paper is the implementation of an algorithm that is able to determine whether an eye is affected or not by keratoconus. The KeratoDetect algorithm analyzes the corneal topography of the eye using a convolutional neural network (CNN) that is able to extract and learn the features of a keratoconus eye. The results show that the KeratoDetect algorithm ensures a high level of performance, obtaining an accuracy of 99.33% on the data test set. KeratoDetect can assist the ophthalmologist in rapid screening of its patients, thus reducing diagnostic errors and facilitating treatment.

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International audience— This paper presents an easy-to-use sensor aimed for traffic safety applications using visible light communications. A central problem in this area is the design of a suitable sensor able to enhance the conditioning of the signal and to avoid disturbances due to the environmental conditions. The visible light communication sensor proposed in this article addresses these issues and enables a robust communication for short to medium distances. The presentation is focused on hardware aspects and low-level coding techniques. The experimental validation of the proposed sensor has been conducted by analyzing communication performances between a commercial traffic light and the sensor, for distances up to 50 m. The measurements exhibit bit error ratio lower than 10-7 in an outdoor configuration, using two well-known codes (Manchester and Miller) without any error-correcting codes or complex signal processing. The prototype is aimed for automotive applications but other outdoor configurations can also be addressed by slight changes in the system design. Index Terms— infrastructure to vehicle communication, robust sensor, smart lighting systems, vehicle safety applications, visible light communications

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The LoRaWAN communication protocol can be used for the implementation of the IoT (Internet of Things) concept. Currently, most of the information regarding the scalability of the LoRa technology is commercial and deals with the best-case scenario. Thus, we need realistic models, enabling the proper assessment of the performance level. Most of the time, the IoT concept entails a large number of nodes distributed over a wide geographical area, therefore forming a high density, large-scale architecture. It is important to determine the number of collisions so that we can assess the network performance. The present paper aims at assessing the performance level of the LoRaWAN technology by analyzing the number of packet collisions that can occur. Thus, this paper determines the maximum number of LoRa nodes that can communicate with a Gateway considering the LoRaWAN protocol specifications. Furthermore, we have proposed a series of solutions for reducing the number of collisions and increasing the capacity of the communication channel.