In this article we introduce the concepts of minimal prime z-, lter, essential z-, lter and r-, lter. We investigate and study the be-havior of minimal prime z-, lters and compare them with minimal prime ideals and coz-ultra, lters. We show that X is a P-space if and only if every , xed prime z-, lter is minimal prime. It is observed that if X is a @-space then X is a P-space if and only if Z[Mf ] is an r-, lter, for every f 2 C(X). The collection of all minimal prime z-, lters will be topologized and it is proved that the space of minimal prime z-, lters is homeomorphic with the space of coz-ultra, lters. Finally, it is obtained several properties and relations between the space of minimal prime z-, lters and the space of minimal prime ideals in C(X).

In the present paper, we introduce the notions of ,-type and generalized ,--type multi-valued contractive mappings in a Menger PbM-space and obtain some new , xed point theorems for both ,-admissible and (, , )-admissible mappings. Our results extensively gen-eralize previous results in this framework. Furthermore, we support our results by some non-trivial examples and an application.

Variations in the loading of rolling contact components lead to a change in contact forces between surfaces. These forces represent the main cause of rolling contact damages such as fatigue. Residual stresses represent a major issue in railway wheel structures, and it is appropriate to reduce such stresses. This paper aims to estimate residual stresses in railway wheel due to hub-to-rim and axle-to-hub  tting processes. A three-dimensional nonlinear model of stress is applied to analyze a stress  eld during the press  tting process. An elastic-plastic  nite-element model is developed to model variable thermal loading in railway wheel. Finally, results of three-dimensional  niteelement analysis showed good agreement with  eld observations.

The main goal of the present paper is to construct some families of the Carlitz's q-Bernoulli polyno-mials and numbers. We  rstly introduce the modi ed Carlitz's q-Bernoulli polynomials and numbers with weight (p. We then de ne the modi ed degenerate Carlitz's q-Bernoulli polynomials and num-bers with weight ( ;  ) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modi ed Carlitz's q-Bernoulli polynomials with weight ( ;  ), the modi ed degenerate Carlitz's q-Bernoulli polynomials with weight ( ;  ), the Stirling numbers of the  rst kind and second kind.

The present paper aims at investigating the manner of two dissipative massive scalar  elds. Two massive scalar  elds that interact with a reservoir were con-sidered and a reservoir was modeled by continuum Klein-Gordon  elds. The Lagrangian of the total system was canonically quantized and the dynamics of the system was de-termined using the Euler-Lagrange equation. Then, the explicit form of the quantum massive scalar  elds in long-time limit were observed. The propagator of the system and correlation functions were calculated at  nite temperature in the thermo eld dynamics formalizem.

In this paper, we de ne the concept of probabilistic like Menger (probabilistic like quasi Menger) space (brie y, PLM-space (PLqM-space)). We present some coupled  xed point and  xed point results for certain contraction type maps in partially order PLM-spaces (PLqM-spaces).

Collagen network is one of Articular Cartilage (AC) vital components that contributes to the depth-dependent and anisotropic responses of the tissue. Since it is computationally expensive to simulate all the structural details of the AC network, they are typically simpli ed in numerical analysis. In particular, the so-called arcade-like structure, which has been widely used in previous complex simulations, does not capture the rotations of  brillar bundles. In this study, the role of such possible rotations in the AC mechanical response was investigated by a set of advanced, biphasic, and parametric Finite Element (FE) simulations of indentation tests. The obtained results indicated the in uence of Fibrillar Rotations (FRs) on the mechanical response by increasing the  brillar stress while regionally a ecting the stress in the upper layers of the AC tissue. On the contrary, FR did not signi cantly alter the tissue elasticity and consequently, might be safely ignored in pure contact mechanical problems. It can be concluded that the excessive FR might regionally increase the stress, which could have a degenerative e ect on the collagen constituent; therefore, it should not be neglected in the related future studies, in which the upper AC layers would resist high permanent shear strains.

One of the most important parameters in designing sewer structures is the ability to accurately simulate their discharge and velocity  eld. Among the various sewer receiving in ow methods, open-channel junctions are the most frequently utilized ones. Because of the existence of separation and contraction zones in the open-channel junctions, the uid ow has a complex behavior. Modeling is carried out by Radial Basis Function (RBF) neural network, Gene Expression Programming (GEP), and Multiple Non-Linear Regression (MNLR) methods. Finding the optimum situation for GEP and RBF models is done by examining various mathematical and linking functions for GEP, di erent numbers of hidden neurons, and various spread amounts for RBF. In order to use the models in practical situations, three equations were conducted by using the RBF, GEP, and MNLR methods in modeling the longitudinal velocity. Then, the surface integral of the presented equations was used to simulate the ow discharge. The results showed that the GEP and RBF methods performed signi cantly better than the MNLR in open-channel junction characteristics simulations. The GEP method had better performance than the RBF in modeling the longitudinal velocity  eld. However, the RBF presented more reliable results in the discharge simulations.