A Study of monogenity of Binomial Composition

Let $\theta$ be a root of a monic polynomial $h(x) \in \Z[x]$ of degree $n \geq 2$. We say $h(x)$ is monogenic if it is irreducible over \Q and $\{ 1, \theta, \theta^2, \ldots, \theta^{n-1} \}$ is a basis for the ring $\Z_K$ of integers of K = \Q(\theta). In this article, we study about the monogenity of number fields generated by a root of composition of two binomials. We characterise all the primes dividing the index of the subgroup $\Z[\theta]$ in $\Z_K$ where K = \Q(\theta) with $\theta$ having minimal polynomial $F(x) = (x^m-b)^n - a \in \Z[x]$, $m\geq 1$ and $n \geq 2$. As an application, we provide a class of pairs of binomials $f(x)=x^n-a$ and $g(x)=x^m-b$ having the property that both $f(x)$ and $f(g(x))$ are monogenic.Comment: 9 page

Anatomical study of nutrient foramen in lower limb dry long bones

Background: Nutrient artery gain access through nutrient foramen and provide vascular supply to bone. Number, size and location of nutrient foramen has significant medical as well as surgical importance. Any insult to nutrient artery during surgical procedure or during trauma may lead to devascualarization or poor prognosis.Methods: The present study consist of 50 femurs, 50 tibia and 50 fibula, collected from department of anatomy, BPKIHS. Mean length of bone, number, position and size and foraminal index of nutrient foramen was observed and recorded accordingly.Results: In femur 62% bone shows single nutrient foramen. Nutrient foramen was commonly located in medial lip of linea aspera and in upper third of bone which was noted in 80% of bone. In tibia 82% of total bone shows single foramen with absent of foramen in 6% bone. Foramen was commonly located above the soleal line and middle third of bone which was noted in 56% of bone. In fibula 6% of total bone shows absent of nutrient foramen and majority of bone shows single nutrient foramen (82%). Foramen was commonly located in lower part of posterior surface (60%) and in middle third of bone.Conclusions: This study provides details topographic knowledge about nutrient foramen which is important clinically for proper planning of surgery and its outcome

Anaesthetic considerations in patients with transverse myelitis

Transverse myelitis is an acute or subacute inflammatory disorder involving the spinal cord. Clinical signs are due to the involvement of the ascending and descending tracts in the transverse plane of the spinal cord. The most common cause is autoimmune. These patients may present with various clinical findings with which it is important for the anaesthesiologist to be familiar in order to manage such cases during the intraoperative and postoperative period. This report discusses issues relating to management of such cases

The prospects of decentralised solar energy home systems in rural communities : User experience, determinants, and impact of free solar power on the energy poverty cycle

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Association Between Body Mass Index, Flat Foot And Knock-Knee Of Physical Education Students Of Guru Ghasidas Vishwavidyalaya, Bilaspur Chhattisgarh

Objective: The purpose of this study was to assess the association between body mass index, flat foot and knock-knee of physical education students of Guru Ghasidas Vishwavidyalaya, Bilaspur Chhattisgarh. Methodology: The sample consisted of 125 university students, in the age category of 20 – 26 Years. Measurement: - BMI: for taken the weight of the student electronic weight machine was use weight in kilogram, Height: for taken the height of the student’s measure by stadiometer in centimetre. Flatfoot: calculated by manually. Foot print taken on the paper, where as foot print divided into three sections A, B & C, and then the widest part of the foot divided by the narrowest part of the foot. Knock-knee:  for identify the knock-knee stand naturally with bare legs together. If there is knocking kneed, the knees should rotate slightly inwards until they touch, with the ankles separated. Statistical analysis: To find out the association between the BMI flatfoot and knock-knee Pearson correlation employed. The level of significant was set at 0.01. Result and discussion: The result showed a significant difference between the BMI and flatfoot and no significance difference with knock-knee among the physical education students of Guru Ghasidas Vishwavidyalaya, bilaspur Chhattisgar

Vertiport Terminal Scheduling and Throughput Analysis for Multiple Surface Directions

Vertical Take-Off and Landing (VTOL) vehicles have gained immense popularity in the delivery drone market and are now being developed for passenger transportation in urban areas to efficiently enable Urban Air Mobility (UAM). UAM aims to utilize the urban airspace \hidetxt{vertical dimension} to address the problem of heavy road congestion in dense urban cities. VTOL vehicles require vertiport terminals for landing, take-off, passengers boarding or deboarding, refuelling (or charging), and maintenance. An efficient scheduling algorithm is essential to maximize the throughput of the vertiport terminal (vertiminal)\hidetxt{ as well as efficient use of airspace} while maintaining safety protocols to handle the UAM traffic. While traditional departure and taxiing operations can be applied in the context of vertiminal, specific algorithms are required for take-off and landing schedules. Unlike fixed-wing aircraft that require a runway to take-off and climb in a single direction, VTOL vehicles can approach and climb in several directions. We propose a Mixed Integer Linear Program (MILP) formulation to schedule flights for taxiing, climbing (or approaching) using multiple directions after take-off (before landing) and turnaround on gates. We also derived equations to thoroughly analyze the throughput capacity of a vertiminal considering all its core elements. We have shown that our MILP can achieve the maximum throughput obtained through the equations. Given the input parameters, our analysis can be used to analyze the capacity of a vertiminal without running any simulation, while our MILP can be used to get the most efficient schedule.Comment: Extension of conference work "Integrated Taxiing and TLOF pad Scheduling Using Different Surface Directions with Fairness Analysis" published in ITSC 2023. DOI: https://doi.org/10.1109/ITSC57777.2023.1042248

Closed Form Expressions for Delay to Ramp Inputs for On-Chip VLSI RC Interconnect

In high speed digital integrated circuits, interconnects delay can be significant and should be included for accurate analysis. Delay analysis for interconnect has been done widely by using moments of the impulse response, from the explicit Elmore delay (the first moment of the impulse response) expression, to moment matching methods which creates reduced order trans impedance and transfer function approximations. However, the Elmore delay is fast becoming ineffective for deep submicron technologies, and reduced order transfer function delays are impractical for use as early-phase design metrics or as design optimization cost functions. This paper describes an approach for fitting moments of the impulse response to probability density functions so that delay can be estimated accurately at an early physical design stage. For RC trees it is demonstrated that the inverse gamma function provides a provably stable approximation. We used the PERI [13] (Probability distribution function Extension for Ramp Inputs) technique that extends delay metrics for ramp inputs to the more general and realistic non-step inputs. The accuracy of our model is justified with the results compared with that of SPICE simulations. Keywords¾ Moment Matching, On-Chip Interconnect, Probability Distribution function, Cumulative Distribution function, Delay calculation, Slew Calculation, Beta Distribution, VLSI

Burden of anxiety in Adolescent: A community-based study in Western Uttar Pradesh

Background: Anxiety is a prevalent issue among adolescents and can adversely affect their academic performance and everyday functioning. Aims & Objectives: To estimate the prevalence of anxiety among adolescents in urban and rural areas and to study the socio-demographic correlates of anxiety among adolescents in urban and rural areas. Methods: A comprehensive survey was conducted in the field practice area of Department of Community Medicine of a Medical College in western district of Uttar Pradesh. The survey was aimed at young people between the ages of 10 and 19 who lived in the practice area of the medical college. Result: The burden of anxiety was observed to be 19.6 % (n=92). Female gender, urban residence, early adolescent age-group (10-13 yr), nuclear family, day-time somnolence and family history of mental illness were factors having statistical significance. Poor education level of parents was also statistically significant. Physical activity and substance abuse did not have significant contribution in burden of anxiety. Conclusion: Anxiety in adolescents is a significant issue influenced by various factors. Early intervention and support are crucial

Simple Acrylic Color Technique for the Preparation of Wet Specimen in Anatomy Museum

INTRODUCTION: The subject anatomy is an essential subject in medical college for students and museum with attractive, an innovative colored specimen with well-labeled specimen aids a pivotal role for teaching and learning process. Once the specimen has been selected for coloring, undergoes fixation, acrylic paint coloring, plastic bottle mounting and proper labeling for better visualization of the structure. MATERIALS & METHOD: We have utilized a simple acrylic color method for painting the gross specimen available for teaching and learning process from well-embalmed cadavers. The materials required are acrylic color paint, brush, clear nail polish, glycerin, clear plastic bottle, 10% formaldehyde and can be performed at room temperature. RESULT: The acrylic coloring technique of wet specimen makes specimen attractive which is cost-effective, non-toxic, creates great interest and aids long term memory to the student. CONCLUSION: The acrylic painted wet gross specimen with clear plastic bottle mounting remains stable in 10% formalin without color fading and makes students a better understanding of the subject.   KEYWORDS: Color specimen, Anatomy museum preparation, Acrylic painting, Plastic mountin

Twelfth rib syndrome: role of intercostal blocks: case series of 10 patients

Twelfth rib syndrome (TRS) is a rare condition that causes severe pain in the loin. It is often misdiagnosed, leading to unnecessary investigations and treatments. Intercostal blocks in the 11th and 12th rib often resolve the pain for these patients. In this research paper, we aim to explore the role of intercostal block in the management of TRS based on our experience with 10 patients. Data of patients who were diagnosed with TRS were studied retrospectively from our hospital records who have been given intercostal block injection from the period of Jan 2022 to August 2023 as an audit.  Four patients underwent intercostal blocks. VAS scores were measured in follow-up for 1 and 3 months. 4 patients were lost to follow up and hence not considered in this study. The male to female ratio was 7:3. There was a statistically significant reduction in VAS score at 1 month and 3 months compared to pre-injection times. Patients who have failed conservative management for TRS can be effectively managed with intercostal block injections