Some periodic and fixed point theorems on quasi-b-gauge spaces

The notions of a quasi-b-gauge space $(U,\textsl{Q}_{s ; \Omega })$ ( U , Q s ; Ω ) and a left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -family of generalized quasi-pseudo-b-distances generated by $(U,\textsl{Q}_{s ; \Omega })$ ( U , Q s ; Ω ) are introduced. Moreover, by using this left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -family, we define the left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -sequential completeness, and we initiate the Nadler type contractions for set-valued mappings $T:U\rightarrow Cl^{\mathcal{J}_{s ; \Omega }}(U)$ T : U → C l J s ; Ω ( U ) and the Banach type contractions for single-valued mappings $T: U \rightarrow U$ T : U → U , which are not necessarily continuous. Furthermore, we develop novel periodic and fixed point results for these mappings in the new setting, which generalize and improve the existing fixed point results in the literature. Examples validating our obtained results are also given.

Strength and life estimation for assigning the useful life of wheelpairs of high-speed flat wagons

Aim. The most vital unit of railway rolling stock is a wheelpair, as a broken wheel or axle may have catastrophic consequences. Therefore, before the production of a highspeed flat wagon designed for operation at speeds of up to 140 km/h, which is unique for the 1520 mm gauge space, could commence, it was required to research the applicability of the standard wheelpair for high-speed movement. Ensuring the safe operation of a wheelpair involves compliance with the requirements that are to be confirmed by means of assessment of strength and durability parameters [1]. Product conformity assessment may be based on the requirements of standards, whose voluntary fulfilment ensures compliance with [1], or other documents. Methods. The paper describes the computational and experimental methods used for confirming the strength and estimating the life (durability) of wheelpair elements in the probabilistic setting. As experimental data, the authors used the results of full-scale bench testing of wheelpairs for fatigue using the method of rotational bending as it best approximates the loading conditions in operation. The results confirmed the endurance limits of the axle and wheel as parts of an assembled wheelpair. Using design analysis, the authors examined the stress-strain state of the wheelpair caused by installation and operational loads in various running modes. Results. The conducted studies confirmed the wheelpair’s compliance with the requirements of [1–3] in terms of safety factors of fatigue strength and endurance, which eliminates the possibility of hazardous situations in the course of high-speed flat wagon operation. The time to fatigue crack nucleation in wheelpair components was evaluated using the fatigue resistance figures of the parts and equivalent amplitudes of dynamic stress caused by operational loads. It appears that this assessment allows establishing – with the assumed probability of destruction – the assigned useful life of a wheelpair axle at 32 years, which corresponds to the assigned useful life of the flat wagon according to the combined criterion. Corresponding standards and regulations required for developing the container-carrying flat wagon are being updated and a new State Standard is being developed. Conclusion. The conducted conformity assessment established that the flat wagon wheelpair meets the safety requirements of [1] and ensures the absence of unacceptable risks associated with harm to life and health of people, animals and plants, the environment and property of individuals and companies in the course of flat wagon operation.

Space Closure Rate in Mandibular Canine Retraction by Elastomeric Power Chain: A Clinical Trial

Background : On a daily basis, orthodontic patients present with malocclusions and orofacial imbalance. Often times, teeth must be extracted in order to obtain proper esthetics, occlusion, and stability as well as extraction of teeth is often a need to close residual space, after the initial decrowding and aligning. Pre adjusted fixed orthodontic appliances commonly utilize sliding mechanics for space closure with different types of force delivery systems. A variety of materials have been used as force delivery systems to close spaces between teeth as in the case of canine retraction after the extraction of premolars. Elastomeric auxiliaries are relatively consistent in producing tooth movements. The purpose of the study to evaluate the rate of mandibular canine retraction by elastomeric power chain. Materials and methods : This obervational study was designed as split mouth study. A total number of 20 patients (40 quadrants),who required canine retraction into first premolar extraction sites as part of their orthodontic treatment in the Department of Orthodontics, BSMMU as study population. The quadrants were affixed by elastomeric power chain (Dentaurum) with 200gm force measured by Correx Tension Gauge. Space closure was measured by means of direct measurement from the mesial surface of mesial wing of the 2nd premolar bracket and the distal surface of distal wing of the canine bracket with digital Vernier Calipers. Results: Mean space closer rate in mandibular canine retraction was 0.99 ± 0.08 mm/month in elastomeric power chain method with p value<0.001. Conclusion : This study revealed that space closer rate in mandibular canine retraction was 0.99 ± 0.08 mm/month by elastomeric power chain. Chatt Maa Shi Hosp Med Coll J; Vol.20 (2); July 2021; Page 28-31

Quantale-Valued Uniformizations of Quantale-Valued Generalizations of Approach Groups

We introduce the categories of quantale-valued approach uniform spaces and quantale-valued uniform gauge spaces, and prove that they are topological categories. We first show that the category of quantale-valued uniform gauge spaces is a full bireflective subcategory of the category of quantale-valued approach uniform spaces and; second, we prove that only under strong restrictions on the quantale these two categories are isomorphic. Besides presenting embeddings of the category of quantale-valued metric spaces into the categories of quantale-valued approach uniform spaces as well as quantale-valued uniform gauge spaces, we show that every quantale-valued approach system group and quantale-valued gauge group has a natural underlying quantale-valued approach uniform space, respectively, a quantale-valued uniform gauge space.

Phenomenological theory of Superconductivity in the frameworks of QCD and RCD

Carrying out the study of phenomenological theory of superconductivity at microscopic level in the framework of QCD and restricted chromodynamics, we have investigated the topology of dyons in magnetic gauge space and showed that RCD vavuum containing plasma of dyons and anti-dyons behave like a chromomagnetic superconductor within which the chromomagnetic gluons propagate in the non-perturbative vacuum. Study of the superconductivity, dual superconductivity and color superconductivity have shown to automatically incorporate the condensation of monopoles or dyons ultimately leading to superconducting confining phases of the QCD vacuum.

Phenomenological theory of Superconductivity in the frameworks of QCD and RCD

Carrying out the study of phenomenological theory of superconductivity at microscopic level in the framework of QCD and restricted chromodynamics, we have investigated the topology of dyons in magnetic gauge space and showed that RCD vavuum containing plasma of dyons and anti-dyons behave like a chromomagnetic superconductor within which the chromomagnetic gluons propagate in the non-perturbative vacuum. Study of the superconductivity, dual superconductivity and color superconductivity have shown to automatically incorporate the condensation of monopoles or dyons ultimately leading to superconducting confining phases of the QCD vacuum.