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.

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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