On the C∗ -algebra valued G-metric space related with fixed point theorems

There are many fixed point results in the various kinds of metric spaces such as b - metric spaces, quaternion metric spaces, G-metric spaces, uniform spaces, non - commutative Banach spaces etc. In this work, we consider the one of modern methods as C*-algebra G-metric space with fixed point theory to solve problems above mentioned. We prove the fixed point theorems for a mapping under the contractive conditions in C*-algebra G-metric space. Besides, we establish the not only existence but also uniqueness theorem of fixed point in the such space. Also, we provide several examples to put support behind our main result

Drug-resistant HIV-1 protease regains functional dynamics through cleavage site coevolution

Drug resistance is caused by mutations that change the balance of recognition favoring substrate cleavage over inhibitor binding. Here, a structural dynamics perspective of the regained wild-type functioning in mutant HIV-1 proteases with coevolution of the natural substrates is provided. The collective dynamics of mutant structures of the protease bound to p1-p6 and NC-p1 substrates are assessed using the Anisotropic Network Model (ANM). The drug-induced protease mutations perturb the mechanistically crucial hinge axes that involve key sites for substrate binding and dimerization and mainly coordinate the intrinsic dynamics. Yet with substrate coevolution, while the wild-type dynamic behavior is restored in both p1-p6 ((LP) (1\u27F)p1-p6D30N/N88D) and NC-p1 ((AP) (2) (V)NC-p1V82A) bound proteases, the dynamic behavior of the NC-p1 bound protease variants (NC-p1V82A and (AP) (2) (V)NC-p1V82A) rather resemble those of the proteases bound to the other substrates, which is consistent with experimental studies. The orientational variations of residue fluctuations along the hinge axes in mutant structures justify the existence of coevolution in p1-p6 and NC-p1 substrates, that is, the dynamic behavior of hinge residues should contribute to the interdependent nature of substrate recognition. Overall, this study aids in the understanding of the structural dynamics basis of drug resistance and evolutionary optimization in the HIV-1 protease system

Extended q-Dedekind-type Daehee-Changhee sums associated with extended q-Euler polynomials

In the present paper, we aim to specify a p-adic continuous function for an odd prime inside a p-adic q-analog of the extended Dedekind-type sums of higher order according to extended q-Euler polynomials (or weighted q-Euler polynomials) which is derived from a fermionic p-adic q-deformed integral on Z(p)

An Algorithm for Explicit Form of Fundamental Units of Certain Real Quadratic Fields and Period Eight

In this paper, we have given an explicit formulation to determine the form of the fundamental units of certain real quadratic number fields. This new algorithm for such quadratic fields is first in the literature and it gives us a more practical way to calculate the fundamental unit. Where, the period in the continued fraction expansion of the quadratic irrational number of the certain real quadratic fields is equal to 8

Evaluation of the effects of selective laser trabeculoplasty on anterior segment parameters by anterior segment optical coherence tomography

WOS:000495711900001PubMed: 31713002To prospectively examine the effects of selective laser trabeculoplasty (SLT) on the anterior chamber angle (ACA) and its related parameters using anterior segment-optic coherence tomography (AS-OCT). Fifty eyes of 50 patients with primary open angle glaucoma (POAG) and ocular hypertension were included in the study. AS-OCT was performed before SLT application, immediately after and at 1 day and 1 month. Intraocular pressure (IOP), central corneal thickness (CCT) and anterior chamber depth (ACD) were also recorded and evaluated. No statistically significant difference was determined in ACA and other AS-OCT parameters (AOD, angle opening distance at 500 and 750 mm; TISA, trabecular-iris space area at 500 and 750 mm) before and 1 day after SLT application (p > 0.05). However, a statistically significant increase was determined in both the temporal and nasal ACA, AOD and TISA values between the baseline and day 30 (p 0.05). SLT resulted in an increase in ACA, AOD and TISA when evaluated using AS-OCT. We think that this study provides a different perspective concerning the effects of SLT in the angle region and the involved mechanism

A new survey to the nonlinear electrical transmission line model

In this paper, we find new travelling wave solutions to the nonlinear electrical transmission line model. Exponential function method is applied. This model is used to the voltage behaviors in electrical transmission lines. Under a suitable choice of control parameters, we plot the figures along with contour surfaces of new solutions by using computational programs such as Mathematica, Maple and Matlab. Some information about the behavior of voltage on the electrical lines is extracted. The hyperbolic, periodic or singular properties are reported

BRCA1, C-erbB-2, and H-ras gene expressions in young women with breast cancer - An immunohistochemical study

Young age does not seem to be directly related to the aggressiveness of the disease among patients with breast cancer. Identification and analysis of the alterations in a susceptibility gene expression in breast cancer occurring in young women may allow identification of those patients in whom tumors will show an aggressive clinical course. The purpose of the present study was to evaluate the association of BRCA1, H-rns, and c-erbB-2 gene expression with clinicopathologic parameters of prognosis in breast cancer. Formalin-fixed, paraffin-embedded tissue from 35 patients with breast cancer younger than 35 years were immunohistochemically stained for BRCA1, H-ras, and c-erbB-2 expression with monoclonal antibodies. For each antibody, immunoreactivity was assessed by a semiquantitative scoring system. Each case was also graded according to the modified Bloom-Richardson criteria and evaluated for Ki-67 labeling index, hormonal status, tumor size, distant metastasis, and axillary lymph node involvement. Strong expression of c-erbB-2 and H-ms were observed in 9 cases (25.7%) and 13 cases (37.2%), respectively. Loss of BRCA1 expression was found in five cases (14.3%). Statistical analysis showed that loss of BRCA1 expression was significantly associated with higher Ki-67 labeling index and greater tumor size. In addition, stronger H-ras expression was significantly associated with lymph node involvement and distant metastasis. However, c-erbB-2 immunoreactivity did not show statistical significance with any prognostic parameters. We conclude that, although care must be taken not to overstate the importance of our results in view of the lack of information on clinical outcome, alterations in BRCA1 and H-ras gene expression might be of prognostic importance because of the role of H-ras protein on metastatic behavior and the role of BRCA1 protein on tumor growth. However, c-erbB-2 expression seems to be of no importance in the prognosis of breast cancer occurring in young women

Transoral endoscopic thyroidectomy vestibular approach (TOETVA): A novel surgical technique for scarless thyroidectomy in pediatric surgery

Transoral endoscopic thyroidectomy vestibular approach (TOETVA) is a novel surgical technique in thyroid surgery that provides a feasible opportunity to avoid a visible neck scar. In recent years, TOETVA became popular in the thyroid surgery of selected adult patients with cosmetic concerns. We conducted a right lobectomy with the TOETVA technique in a 17-year-old adolescent with a suspicious thyroid nodule the present report aimed to describe the details of the operative technique step by step. Level of evidence: LEVEL IV, case series with no comparison group (c) 2022 Elsevier Inc. All rights reserved