Prime Root Research Articles

𝑝-DG Cyclotomic nilHecke Algebras

We categorify a tensor product of two Weyl modules for quantum s l 2 \mathfrak {sl}_2 at a prime root of unity.

𝑝-DG Cyclotomic nilHecke Algebras II

We categorify tensor products of the fundamental representation of quantum s l 2 \mathfrak {sl}_2 at prime roots of unity, building upon earlier work where a tensor product of two Weyl modules was categorified.

Inclusive Innovations in Forensic Epistemology and Pedagogy: A Proposed Framework

Scientific temper in evidence processing using forensic knowledge reposes public faith in justice system. Forensic science is a blend of various disciplines, including art, pure sciences, and humanities, with experiment-oriented scientific validation. Forensics and law are intertwined precepts enabling translational impact on the legal system in pursuit of truth to ensure flawless justice. Worldwide, forensics intensely involves both doctrinal and clinical perspectives, largely converging on scientific theories and laboratory experiments to construe expert opinion, and similar pedagogy must be adopted in India as envisaged under the New Education Policy-2020. 3 In legal parlance, forensic inputs are secondary evidence, but primarily used for corroboration for exploring missing links in the chain of events. Due to multi-disciplinary content knowledge sharing during forensic studies, though fascinating, poses pedagogical challenges. Globally, imparting significance of procedural law, the backbone of forensic evidence, is largely missing from forensic education. Expert opinion is contested in courtrooms on ground of admissibility in terms of reliability and validity including protection of chain of custody necessary to avoid manipulation or tampering of samples which is prime root cause for miscarriage of justice. This article deliberates upon an entwined framework of epistemology and pedagogy for imparting holistic understanding of law and science in forensic education. We propose three verticals for forensic pedagogy: (i) crime scene management for scientific handling of articles and traces; (ii) laboratory experimentation and forensic report writing and (ii) translating expert opinion into legal evidence and its presentation during the court proceedings.

Deferment Roots in Building Formation and Construction Projects in South-eastern Nigeria

Deferment in the course of building formation and construction projects is an aspect of the shared situations in the formation stage of the building industry, several factors like timing, availability of raw material, delay in down payment, and readiness of finance, construction goodwill and building logistics. This study is aimed at determining the prime roots of deferments in the formation stage of building projects in South-eastern Nigeria. Research study approach was engaged throughout the sampled urban areas in South-eastern Nigeria, for instance: Aba, Abakalikki, Owerri, and Awka. 150 copies of well-completed questionnaires were collected and analyzed. The outcome specified that disparities roots, deferments in stage-to-stage overheads, bidding below cost price, and subcontractors’ weak execution, and complications in communication were fundamental to the deferments in the execution of building projects in South-eastern Nigeria. This study is the foremost on the roots of deferments in the formation stage of building projects in South-eastern Nigeria. The relative study revealed two exceptional roots of deferments in the Nigerian building industry, for instance, pressure in demanding job safety, and irrational demand for advance disbursements by constructors. It also discloses diverse categories of deferment roots in accordance by means of notable civil and financial situations in South-eastern Nigeria. Conclusively, the result from the study is not only applicable to South-eastern Nigeria but can be extended to building construction projects in other parts of the developing nations of the world for similar outcomes. Keywords: Deferments; building projects; hazard supervision; South-eastern Nigeria, building formation; relative study; building construction.

Categorifying Hecke algebras at prime roots of unity, part I

We equip the type A A diagrammatic Hecke category with a special derivation, so that after specialization to characteristic p p it becomes a p p -dg category. We prove that the defining relations of the Hecke algebra are satisfied in the p p -dg Grothendieck group. We conjecture that the p p -dg Grothendieck group is isomorphic to the Iwahori-Hecke algebra, equipping it with a basis which may differ from both the Kazhdan-Lusztig basis and the p p -canonical basis. More precise conjectures will be found in the sequel. Here are some other results contained in this paper. We provide an incomplete proof of the classification of all degree + 2 +2 derivations on the diagrammatic Hecke category, and a complete proof of the classification of those derivations for which the defining relations of the Hecke algebra are satisfied in the p p -dg Grothendieck group. In particular, our special derivation is unique up to duality and equivalence. We prove that no such derivation exists in simply-laced types outside of finite and affine type A A . We also examine a particular Bott-Samelson bimodule in type A 7 A_7 , which is indecomposable in characteristic 2 2 but decomposable in all other characteristics. We prove that this Bott-Samelson bimodule admits no nontrivial fantastic filtrations in any characteristic, which is the analogue in the p p -dg setting of being indecomposable.

Genetic diversity among two native Indian chicken populations using cytochrome c oxidase subunit I and cytochrome b DNA barcodes.

Background and Aim:India has large varieties (recognized, unrecognized) of native chickens (Desi) scattered throughout the country, managed under scavenging system different from commercial chicken breeds. However, they are less investigated for genetic diversity they harbor. The present study was planned to evaluate genetic diversity among two native chicken populations of North Gujarat (proposed Aravali breed) and South Gujarat (Ankleshwar breed). Aravali chicken, a distinct population with unique characters different from the registered chicken breeds of India is under process to be registered as a new chicken breed of Gujarat, India.Materials and Methods:Two mitochondrial markers, namely, cytochrome oxidase c subunit I (COX I) and cytochrome b (Cyt b) genes were studied across 10 birds from each population. Methodology included sample collection (blood), DNA isolation (manual), polymerase chain reaction amplification of mitochondrial genes, Sanger sequencing, and purification followed by data analysis using various softwares.Results:Haplotype analysis of the COX I gene unveiled a total eight and three haplotypes from the Aravali and Ankleshwar populations, respectively, with haplotype diversity (Hd) of 92.70 % for the Aravali and 34.50% for the Ankleshwar breed. Haplotype analysis of the Cyt b gene revealed a total of four haplotypes from the Aravali population with 60% Hd and no polymorphism in Ankleshwar breed. The phylogenetic analysis uncovered Red Jungle Fowl and Gray Jungle Fowl as prime roots for both populations and all domestic chicken breeds.Conclusion:Study findings indicated high genetic variability in Aravali chicken populations with COX I mitochondrial marker being more informative for evaluating genetic diversity in chickens.

Burns Management In Tertiary Health Care Centre

In rural places of our country, burns have become frequent accidents due to the use of floor-based stoves & kerosene lamps. Suicides due to burns are also quite usual in our country. The objective of this study is to evaluate the necessity of early excision of the burn wound and skin grafting to decrease the morbidity, mortality, complications of burns and stay at the hospital. Calculate pressure garment efficacy in preventing burn scar and contracture formation. To lay out cost-effective management for patients at rural hospitals. 50 patients were included in this study presenting with burn injuries, admitted in the department of plastic surgery from June 2019 to December 2020. In a recent study, Females (52%) suffered more as compared to males. Scalds were the prime root cause of the burns constituting the 52% of the cases. Infections of Burn wound was seen in 20 patients (40%). Pseudomonas was prime organism isolated. Wound excision was required in 19 patients (38%). Around 6 to 12 days, elapsed between the injury to the surgical excision. 19 patients required (38%) covering of wound permanently with STSG. The mean admission period in hospital for burns of 41-60% was 62 days, 33.4 days for 21-40% burns and 19.6 days for <20%. Amongst 50 patients, 3 died accounting to 6% of overall cases. This study concluded that initiation of resuscitation with untimely wound excision and permanent coverage with grafting can bring significant fall in mortality, painful debridements, limiting complications, decreasing the duration of stay at a hospital, curtailing the cost of health care and time apart from work.

Mechanistic Insights into the Oxidized Low-Density Lipoprotein-Induced Atherosclerosis.

Dyslipidaemia has a prominent role in the onset of notorious atherosclerosis, a disease of medium to large arteries. Atherosclerosis is the prime root of cardiovascular events contributing to the most considerable number of morbidity and mortality worldwide. Factors like cellular senescence, genetics, clonal haematopoiesis, sedentary lifestyle-induced obesity, or diabetes mellitus upsurge the tendency of atherosclerosis and are foremost pioneers to definitive transience. Accumulation of oxidized low-density lipoproteins (Ox-LDLs) in the tunica intima triggers the onset of this disease. In the later period of progression, the build-up plaques rupture ensuing thrombosis (completely blocking the blood flow), causing myocardial infarction, stroke, and heart attack, all of which are common atherosclerotic cardiovascular events today. The underlying mechanism is very well elucidated in literature but the therapeutic measures remains to be unleashed. Researchers tussle to demonstrate a clear understanding of treating mechanisms. A century of research suggests that lowering LDL, statin-mediated treatment, HDL, and lipid-profile management should be of prime interest to retard atherosclerosis-induced deaths. We shall brief the Ox-LDL-induced atherogenic mechanism and the treating measures in line to impede the development and progression of atherosclerosis.

AYURVEDIC MANAGEMENT OF RAKTAPRADARA W.S.R. TO ENDOMETRIAL HYPERPLASIA – A CASE STUDY

Background: Ayurveda got incarnated upon the planet Earth to achieve the good health, which is prime root to perform virtuous acts, to acquire gratification of desires and last but not the least Emancipation. Now adays women are suffering from several gyneacological problems due to their unhealthy diet and life-style but most of the time they ignore their problems, and one of them most of the common problem is Raktapradara; which is characterized by irregular and/or excessive bleeding per vagina, caused not only during menses but may be even during intermenstrual period. Material & Method: A 47year old, married, female patient suffering from heavy vaginal bleeding which is previously diagnosed with Endometrial Hyperplasia in her USG findings, has given Shaman Chikitsa (Pit-tashamak, Vatashamak and Raktastambhak) and Shodhan Chikitsa (nitya virechan) for 3 months. Conclusion: Treatment given to the patient proved very beneficial and quickly acting in the management of Raktapradara.

Cell 2-representations and categorification at prime roots of unity

Motivated by recent advances in the categorification of quantum groups at prime roots of unity, we develop a theory of 2-representations for 2-categories, enriched with a p-differential, which satisfy finiteness conditions analogous to those of finitary or fiat 2-categories. We construct cell 2-representations in this setup, and consider a class of 2-categories stemming from bimodules over a p-dg category in detail. This class is of particular importance in the categorification of quantum groups, which allows us to apply our results to cyclotomic quotients of the categorifications of small quantum group of type sl2 at prime roots of unity by Elias–Qi (2016) [3]. Passing to stable 2-representations gives a way to construct triangulated 2-representations, but our main focus is on working with p-dg enriched 2-representations that should be seen as a p-dg enhancement of these triangulated ones.

A CATEGORIFICATION OF A QUANTUM FROBENIUS MAP

A quantum Frobenius map a la Lusztig for $\mathfrak{s}\mathfrak{l}_{2}$ is categorified at a prime root of unity.

Occurrence of sulfonamide class of antibiotics resistance in Korean paddy soils under long-term fertilization practices

Bacteria and genes that can resist antibiotics are emerging as environmental pollutants, and they need to be dealt with. While a few reports have been published, on veterinary antibiotic resistant bacteria and genes, none has been done on the soils in Korea, where the use of sulfonamides in veterinary antibiotics is prevalent. This is the first study to investigate the prevalence and distribution of sulfonamide (sulfamethoxazole, sulfamethazine, and sulfathiazole)-resistant bacteria and genes in both natural and long-term fertilized (inorganic fertilizer and pig and cattle manure composts) soils in Korea. Three long-term (47 years) fertilized (NPK, pig or cattle manure composts) paddy field soils along with an unfertilized, natural wetland soil of a mountain site collected from South Korea were examined in this study. Antibiotic resistance rates of bacteria in the collected samples were calculated for different concentrations of the sulfonamide class of antibiotics. The antibiotic-resistant bacteria were identified using the matrix-assisted laser desorption/ionization—time of flight or MALDI-TOF identification method at genus and species levels. Soil DNA was extracted, and PCR coupled with gel electrophoresis was done in order to detect sulfonamide resistant genes. Results showed that amendment of antibiotics containing animal manures, particularly from pig farms, may be a prime root cause for the spread and abundance of antibiotic resistance in Korean agricultural soils (cumulative resistance rate of 40 to 95% in the order sulfathiazole > sulfamethazine > sulfamethoxazole). Of the 2444 antibiotic-resistant isolates identified, about 80–95% belonged to Bacillus followed by Arthrobacter and Pseudomonas. Of the 56–58 distinct bacterial species detected in the long-term manure-amended Korean paddy soils, the known endospore-forming B. megatherium was predominant and it is suggested that they contribute to the observed high antibiotic resistance. Further, the sulfonamide-resistant genes [sul(I) and sul(II)] were prevalent in both natural and fertilized soils, confirming the widespread prevalence of the sulfonamide-resistant community in Korean soils. This study demonstrates that applying livestock manure compost to agricultural fields does have a large impact on the occurrence of sulfonamide-resistant bacteria and genes, particularly the ability to increase their prevalence in the environment. This outcome highlights the necessity to regulate the usage of veterinary antibiotics in Korea.

A categorification of quantum [formula omitted] at prime roots of unity

We categorify the Beilinson–Lusztig–MacPherson integral form of quantum sl(2) specialized at a prime root of unity.

A categorification of the Burau representation at prime roots of unity

We construct a p-DG structure on an algebra Koszul dual to a zigzag algebra used by Khovanov and Seidel to construct a categorical braid group action. We show there is a braid group action in this p-DG setting.

Equiangular lines and covers of the complete graph

The relation between equiangular sets of lines in the real space and distance-regular double covers of the complete graph is well known and studied since the work of Seidel and others in the 70s. The main topic of this paper is to continue the study on how complex equiangular lines relate to distance-regular covers of the complete graph with larger index. Given a set of equiangular lines meeting the relative (or Welch) bound, we show that if the entries of the corresponding Gram matrix are prime roots of unity, then these lines can be used to construct an antipodal distance-regular graph of diameter three. We also study in detail how the absolute (or Gerzon) bound for a set of equiangular lines can be used to derive bounds of the parameters of abelian distance-regular covers of the complete graph.

An approach to categorification of some small quantum groups II

We categorify an idempotented form of quantum sl2 and some of its simple representations at a prime root of unity.

An approach to categorification of some small quantum groups

We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.

English

Cross-tolerance is the phenomenon by which a plant resistance to stress results in resistance to another form of stress. Such intriguing links has made the author to suggest that foliar camel urine (CU) application depending on its amazing constituents may mimic elicitor actions and prime tissues to pathogens in normally susceptible host plants. This study was conducted to assess anatomical and biochemical pathogenesis alterations in tomato water T1, Fusarium oxysporum infected T2 plants and also to evaluate the defense-related responses resulting from CU application in either nonT3 and/or T4 infected seedlings at anatomical and molecular levels. Fast and consistent increment in detoxifying enzymes peroxidase, phenylalanine ammonia-lyase, polyphenol oxidase and soluble proteins were recorded in T4 roots. In contrast, tomato roots, T2, T4 showed retard response in catalase activity. T4 accumulate highly significant level (80%) of total free and bound phenolics within its root. Root of T4 SA concomitant with coumarins had significant increment in both free and conjugated phenolic part. Anatomical microscopy shows alterations in T2, T3 as compared to T1 tomato root vascular bundle diameter. Results showed earlier reduction explained as adaptation mechanism in resisting the imposed stress regardless of its type. In contrast, T4 seedlings showed great increase in vascular bundle diameter concomitant with xylem lignin deposition and on epidermis cell walls. Tomato shoot administered CU implicate phenylpropanoid pathway in prime root to F. oxysporum invasion by enhancing innate immunity mechanisms, fast accumulation of H2O2 concomitant with cell wall modifications as physical barrier. Key words: Cross-resistance, signaling, defense mechanism, detoxification enzymes, free and glycoside-phenolics, phenylpropanoid pathway.

Increased scattering efficiency through cell optimization in acoustic diffusers

This presentation will provide test data, experiments, and analysis in showing the interaction of absorption and diffusion characteristics. It will be shown that absorption, either additive or design inherent, has an adverse effect on the efficiency of the acoustic diffusers. The effects of low frequency interference on various cell structures of quadratic residue diffusers will be highlighted as a prime example of this theory. The inclusion of additive absorption, i.e., fabric, fiberglass, and other materials, further complicates the matter of diffuser efficiency. While design characteristics of some diffusers, such as prime root and quadratic residue diffusers, can be used effectively for their absorption coefficients, overall these characteristics detract from the efficiency of the diffusion coefficients. Product designs utilizing optimized cell designs to inhibit absorption in diffusers will be shown. It will be shown that this cell optimization dramatically increases the efficiency of the diffuser. This optimization includes both higher scattering coefficients and smoother frequency responses. Comparative analysis will be provided with traditional designs and newer optimized designs.

Quantum invariants of 3-manifolds: Integrality, splitting, and perturbative expansion

We consider quantum invariants of 3-manifolds associated with arbitrary simple Lie algebras. Using the symmetry principle we show how to decompose the quantum invariant as the product of two invariants, one of them is the invariant corresponding to the projective group. We then show that the projective quantum invariant is always an algebraic integer, if the quantum parameter is a prime root of unity. We also show that the projective quantum invariant of rational homology 3-spheres has a perturbative expansion a la Ohtsuki. The presentation of the theory of quantum 3-manifold invariants is self-contained.