On families of convex polytopes with constant metric dimension

AbstractLet G be a connected graph and d(x,y) be the distance between the vertices x and y. A subset of vertices W={w1,w2,…,wk} is called a resolving set for G if for every two distinct vertices x,y∈V(G), there is a vertex wi∈W such that d(x,wi)≠d(y,wi). A resolving set containing a minimum number of vertices is called a metric basis for G and the number of vertices in a metric basis is its metric dimension dim(G). A family G of connected graphs is a family with constant metric dimension if dim(G) is finite and does not depend upon the choice of G in G.In this paper, we study the metric dimension of some classes of convex polytopes which are obtained by the combinations of two different graph of convex polytopes. It is shown that these classes of convex polytopes have the constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of these classes of convex polytopes

On the metric dimension of rotationally-symmetric convex polytopes

Metric dimension is a~generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let $\mathcal{F}$ be a family of connected graphs $G_{n}$ : $\mathcal{F} = (G_{n})_{n}\geq 1$ depending on $n$ as follows: the order $|V(G)| = \varphi(n)$ and $\lim\limits_{n\rightarrow \infty}\varphi(n)=\infty$. If there exists a constant C > 0 such that $dim(G_{n}) \leq C$ for every $n \geq 1$ then we shall say that $\mathcal{F}$ has bounded metric dimension, otherwise $\mathcal{F}$ has unbounded metric dimension. If all graphs in $\mathcal{F}$ have the same metric dimension, then $\mathcal{F}$ is called a family of graphs with constant metric dimension.\\ In this paper, we study the metric dimension of some classes of convex polytopes which are rotationally-symmetric. It is shown that these classes of convex polytoes have the constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of these classes of convex polytopes. It is natural to ask for the characterization of classes of convex polytopes with constant metric dimension

Impact of employee empowerment on job satisfaction: an empirical analysis of Pakistani service industry

The purpose of this study is to determine the relationship between employee empowerment and job satisfaction in Pakistani service industry. This study also examines the difference between job satisfaction level of male and female employees. The questionnaire consisting twenty four statements was used for collection of data and was distributed among 200 employees of service industries in Pakistan. SPSS was used for analysis. Results indicate that employee empowerment has positive and significant impact on job satisfaction. The results also confirm a significant difference between male and female employees job satisfaction level. Evidence depicts that male employees are more satisfied from their jobs

ASSESSMENT OF RADIOLOGICAL HEALING IN ELDERLY HIP FRACTURES FIXED WITH INTRAMEDULLARY VERSUS EXTRAMEDULLARY IMPLANTS AT THREE MONTHS

OBJECTIVE: To compare the radiological healing in elderly patients with hip fractures fixed with intramedullary versus extramedullary implants at 3 months by using Radiological Union Score for Hip (RUSH score). METHODS: This quasi-experimental study was conducted at Lady Reading Hospital, Peshawar from September 2020 to March 2021, in elderly patients (50-80 years) with hip fractures. Out of 238 patients, 119 were non-randomly assigned to Group-A undergoing intra- medullary implants and 119 to Group-B undergoing fixation with an extra-medullary implant. After the surgery, the patients were followed up periodically at 2nd week, 6th week and 12th week after surgery and assessed for radiological healing through RUSH score. The data was analyzed using SPSS version 23. RESULTS: Out of 238 patients, 96 were males and 142 were females. In Group-A, 51 (42.9%) were males and 68 (57.1%) were females. In Group-B, 45 (37.8%) were males and 74 (62.2%) were females. Majority (n=135/238: 56.72%) were aging from 50-60 years. Mean±SD of age was 63.1±8.8 years and 61.7±8.1 years in Group-A & Group-B respectively. Mean±SD of RUSH score in Group-A & Group-B was 19.50±6.92 and 22.51±5.60 respectively. Mean RUSH score for males in Group-A and Group-B was 21.52±6.39 and 22.33±6.99 (p=0.354) and for females in Group-A and Group-B was 19.36±7.33 and 22.18±5.75 (p=0.025) respectively. Median and IQR of RUSH score in Group-A & Group-B was 21±10 and 23±8 respectively (p=0.069). CONCLUSION: There was statistically insignificant difference in median RUSH score with use of either intramedullary or extramedullary implants in the management of hip fractures

Development of a STEP-compliant design and manufacturing framework for discrete sheet metal bend parts

Metal sheets have the ability to be formed into nonstandard sizes and sections. Displacement-controlled computer numerical control press brakes are used for three-dimensional sheet metal forming. Although the subject of vendor neutral computer-aided technologies (computer-aided design, computer-aided process planning and computer-aided manufacturing) is widely researched for machined parts, research in the field of sheet metal parts is very sparse. Blank development from three-dimensional computer-aided design model depends on the bending tools geometry and metal sheet properties. Furthermore, generation and propagation of bending errors depend on individual bend sequences. Bend sequence planning is carried out to minimize bending errors, keeping in view the available tooling geometry and the sheet material properties’ variation. Research reported in this article attempts to develop a STEP-compliant, vendor neutral design and manufacturing framework for discrete sheet metal bend parts to provide a capability of bidirectional communication between design and manufacturing cycles. Proposed framework will facilitate the use of design information downstream at the manufacturing stage in the form of bending workplan, bending workingsteps and a feedback mechanism to the upstage product designer. In order to realize this vendor neutral framework, STEP (ISO 10303), AP203, AP207, and AP219 along with STEP-NC (ISO14649) have been used to provide a basis of vendor neutral data modeling.N/

Synthesis and characterisation of doxorubicin-loaded functionalised cobalt ferrite nanoparticles and their in vitro anti-tumour activity under an AC-magnetic field

Purpose: To synthesise and evaluate the anti-tumour properties of doxorubicin-loaded xanthan gumfunctionalised cobalt ferrite nanoparticles (CoFe2O4.NPs@XG-Doxo) under an AC-magnetic field.Methods: Multidimensional magnetic cobalt ferrite (CoFe2O4) nanoparticles (NPs) were synthesised by a co-precipitation method. The synthesised cobalt ferrite nanoparticles (CFNPs) were functionalised with xanthine gum (XG) and subsequently characterised by Fourier transform-infrared spectroscopy (FT-IR), thermogravimetric analysis (TGA) and contact angle studies. Vibrating sample magnetometry (VSM) was used for magnetic measurements of the native and XG-coated CFNPs. The microstructural morphology of the uncoated and XG-coated CFNPs was established using scanning electron microscopy (SEM), atomic force microscopy (AFM) and dynamic light scattering (DLS) studies. Finally, the doxorubicin release profile of the drug-loaded functionalised CFNPs was evaluated using an oscillating magnetic field (OMF) apparatus in the presence of an externally applied magnetic field.Results: XG coating decreased the contact angle of the native CFNPs from 92° to 40°, which indicates that it modified the CFNP surface from hydrophobic to hydrophilic. VSM analysis demonstrated that CoFe2O4.NPs@XG also retained the magnetic characteristics of the bare cobalt ferrite nanocrystals, endorsing its application as a promising magnetic nanovector (MNV). The synthesised CoFe2O4.NPs@XG-Doxo exhibited significantly higher controlled discharge of doxorubicin at acidic pH (5.0) than at neutral pH (7.4). In vitro analysis revealed the remarkable lower systematic toxicity of XGcoated CoFe2O4.NPs compared with uncoated CFNPs against Chinese hamster ovary (CHO) and Huh7 cell lines.Conclusion: These results indicate that XG-coated CFNPs are a biocompatible MNV for doxorubicin.Keywords: Cobalt ferrite, Cytotoxicity, Drug delivery, Nanoparticles, Xanthan gu

Photocatalytic response in water pollutants with addition of biomedical and anti-leishmanial study of iron oxide nanoparticles

Public health is a major concern globally, owing to the presence of industrial dyes in the effluent. Nanoparticles with green synthesis are an enthralling research field with various applications. This study deals with investigating the photocatalytic potential of Fe-oxide nanoparticles (FeO-NPs) for the degradation of methylene blue dye and their potential biomedical investigations. Biosynthesis using Anthemis tomentosa flower extract showed to be an effective method for the synthesis of FeO-NPs. The freshly prepared FeO-NPs were characterized through UV/Vis spectroscopy showing clear peak at 318 nm. The prepared FeO-NPs were of smaller size and spherical shape having large surface area and porosity with no aggregations. The FeO-NPs were characterized using XRD, FTIR, HRTEM, SEM and EDX. The HRTEM results showed that the particle size of FeO-NPs was 60–90 nm. The antimicrobial properties of FeO-NPs were investigated against two bacterial Staphylococcus aureus 13 (±0.8) and Klebsiella pneumoniae 6(±0.6) and three fungal species Aspergillus Niger, Aspergillus flavus, and Aspergillus fumigatus exhibiting a maximum reduction of 57% 47% and 50%, respectively. Moreover, FeO-NPs exhibited high antioxidant properties evaluated against ascorbic acid. Overall, this study showed high photocatalytic, antimicrobial, and antioxidant properties of FeO-NPs owing to their small size and large surface area. However, the ecotoxicity study of methylene blue degradation products showed potential toxicity to aquatic organisms

Traditional healers working with primary care and mental health for early intervention in psychosis in young persons: protocol for the feasibility cluster randomised controlled trial

Objectives In low/middle-income countries (LMICs), more than half of patients with first-episode psychosis initially seek treatment from traditional and religious healers as their first care. This contributes to an excessively long duration of untreated psychosis (DUP). There is a need for culturally appropriate interventions to involve traditional and spiritual healers to work collaboratively with primary care practitioners and psychiatrists through task-shifting for early detection, referral and treatment of first episode of psychosis. Methods To prevent the consequences of long DUP in adolescents in LMICs, we aim to develop and pilot test a culturally appropriate and context-bespoke intervention. Traditional HEalers working with primary care and mental Health for early interventiOn in Psychosis in young pErsons (THE HOPE) will be developed using ethnographic and qualitative methods with traditional healers and caregivers. We will conduct a randomised controlled cluster feasibility trial with a nested qualitative study to assess study recruitment and acceptability of the intervention. Ninety-three union councils in district Peshawar, Pakistan will be randomised and allocated using a 1:1 ratio to either intervention arm (THE HOPE) or enhanced treatment as usual and stratified by urban/rural setting. Data on feasibility outcomes will be collected at baseline and follow-up. Patients, carers, clinicians and policymakers will be interviewed to ascertain their views about the intervention. The decision to proceed to the phase III trial will be based on prespecified stop–go criteria. Ethics and dissemination Ethical approval has been obtained from Keele University Ethical Review Panel (ref: MH210177), Khyber Medical University Ethical Review Board (ref: DIR/KMU-EB/IG/001005) and National Bioethics Committee Pakistan (ref no. 4-87/NBC-840/22/621). The results of THE HOPE feasibility trial will be reported in peer-reviewed journals and academic conferences and disseminated to local stakeholders and policymakers. Trial registration number ISRCTN75347421

Effects of a high-dose 24-h infusion of tranexamic acid on death and thromboembolic events in patients with acute gastrointestinal bleeding (HALT-IT): an international randomised, double-blind, placebo-controlled trial

Background: Tranexamic acid reduces surgical bleeding and reduces death due to bleeding in patients with trauma. Meta-analyses of small trials show that tranexamic acid might decrease deaths from gastrointestinal bleeding. We aimed to assess the effects of tranexamic acid in patients with gastrointestinal bleeding. Methods: We did an international, multicentre, randomised, placebo-controlled trial in 164 hospitals in 15 countries. Patients were enrolled if the responsible clinician was uncertain whether to use tranexamic acid, were aged above the minimum age considered an adult in their country (either aged 16 years and older or aged 18 years and older), and had significant (defined as at risk of bleeding to death) upper or lower gastrointestinal bleeding. Patients were randomly assigned by selection of a numbered treatment pack from a box containing eight packs that were identical apart from the pack number. Patients received either a loading dose of 1 g tranexamic acid, which was added to 100 mL infusion bag of 0·9% sodium chloride and infused by slow intravenous injection over 10 min, followed by a maintenance dose of 3 g tranexamic acid added to 1 L of any isotonic intravenous solution and infused at 125 mg/h for 24 h, or placebo (sodium chloride 0·9%). Patients, caregivers, and those assessing outcomes were masked to allocation. The primary outcome was death due to bleeding within 5 days of randomisation; analysis excluded patients who received neither dose of the allocated treatment and those for whom outcome data on death were unavailable. This trial was registered with Current Controlled Trials, ISRCTN11225767, and ClinicalTrials.gov, NCT01658124. Findings: Between July 4, 2013, and June 21, 2019, we randomly allocated 12 009 patients to receive tranexamic acid (5994, 49·9%) or matching placebo (6015, 50·1%), of whom 11 952 (99·5%) received the first dose of the allocated treatment. Death due to bleeding within 5 days of randomisation occurred in 222 (4%) of 5956 patients in the tranexamic acid group and in 226 (4%) of 5981 patients in the placebo group (risk ratio [RR] 0·99, 95% CI 0·82–1·18). Arterial thromboembolic events (myocardial infarction or stroke) were similar in the tranexamic acid group and placebo group (42 [0·7%] of 5952 vs 46 [0·8%] of 5977; 0·92; 0·60 to 1·39). Venous thromboembolic events (deep vein thrombosis or pulmonary embolism) were higher in tranexamic acid group than in the placebo group (48 [0·8%] of 5952 vs 26 [0·4%] of 5977; RR 1·85; 95% CI 1·15 to 2·98). Interpretation: We found that tranexamic acid did not reduce death from gastrointestinal bleeding. On the basis of our results, tranexamic acid should not be used for the treatment of gastrointestinal bleeding outside the context of a randomised trial