Modular Categories Associated to Unipotent Groups

Let G be a unipotent algebraic group over an algebraically closed field k of characteristic p > 0 and let l be a prime different from p. Let e be a minimal idempotent in D_G(G), the braided monoidal category of G-equivariant (under conjugation action) \bar{Q_l}-complexes on G. We can associate to G and e a modular category M_{G,e}. In this article, we prove that the modular categories that arise in this way from unipotent groups are precisely those in the class C_p^{\pm}.Comment: 26 page

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions

Culturally Displaced Identity of the Protagonist in the Novel ‘Wife’

Bharati Mukherjee was an Indian diasporic writer. Though she migrated to USA, her roots have always been in India, associated with the culture and tradition of the native country. As an expatriate writer her works project the cultural displacement faced by the immigrants and the impact that is left on them. Her novels project the different situations the migrated characters face, problems they overcome, the adjustments they make and the feeling of isolation. The present paper discusses the impact of cultural displacement on the main protagonist Dimple das gupta in the novel Wife written by Bharati Mukherjee and published in the year 1975.My objective is to project the problem faced by the first generation of immigrants by studying the character Dimple das gupta and the impact of cultural displacement on the immigrants by using the tools of psycho-analytical theory. Application of Psycho- analytical theory to literary texts helps the readers to study the characters and find out the reasons for different behaviours .According to Sigmund Freud it is clash of id, ego and superego which are the three parts of the human psyche that makes transformation of personalities that result in different behaviors'. If people experience these type of psychological clashes they do not come under normal personality. As the founder of psychiatry Sigmund Freud mentioned the functioning of the mind at various levels in terms of psychology and neurology. The main protagonist Dimple das gupta lives in a fantasy world and makes dream as source of her living in the native country and in the alien country. Her dream takes a violent turn because of the suppressed desires and makes her a negative character. One of the reasons being the cultural displacement. She dreams a beautiful life and a good husband but when her dreams are shattered she kills her husband. She turns out to be a different personality altogether who cannot find happiness in her marriage either in Calcutta or in USA

Advancements in Deep Learning for Early Detection of Plant Diseases: Techniques, Challenges, and Opportunities in Precision Agriculture

Deep learning (DL) has emerged as a transformative technology in the field of agriculture, revolutionizing various applications such as disease recognition, plant classification, and fruit counting. Compared to traditional image processing techniques, deep learning has demonstrated a remarkable ability to achieve significantly higher accuracy, surpassing the performance of conventional methods.One of the primary advantages of leveraging deep learning in agriculture is its unparalleled capacity to provide more precise predictions, enabling farmers and researchers to make better-informed decisions that lead to improved outcomes. Deep learning models have consistently exhibited impressive performance across a wide range of tasks, including visual recognition, language processing, and speech detection, making them highly suitable for diverse agricultural applications. Furthermore, the success of deep learning in medical imaging has been successfully extended to the agricultural domain. By applying deep learning's powerful capabilities, stakeholders in the agricultural sector can now accurately classify plant species, detect diseases, and identify pests with unprecedented precision. This advancement has the potential to drive significant improvements in productivity, reduce crop losses, and optimize resource allocation, ultimately transforming the way we approach agricultural practices

Ground Water Quality Study of KhadkiNala Basin, MangalwedhaTaluka, Solapur District , Maharastra , India

The term ground water quality covers a widespread meaning and is referred by an individual depending on suitability of ground water for intended use. Water gets polluted due to contamination by foreign matter such a chemicals, industrial or other waste or sewage. Disposal of sewage water in to fresh water aquifer is the main cause of ground water pollution. Hence determination of groundwater quality is important to observe the suitability of water for particular use. From last few years there have been many changes occur in KhadkiNala basin region. There has been increase in urbanization

The Effect of Performance Variation on Rater Attributions and Ratings of Job Performance

In most organizations, employee performance is evaluated annually by their supervisors and these evaluations lead to important individual and organizational outcomes. Research has shown that properties of the performance distribution referred to as Gestalt characteristics (e.g., mean, variability) have a significant effect on performance ratings, as well as the attributions that raters make about ratee ability and motivation. This study extends previous research demonstrating the influence of Gestalt characteristics on performance ratings by examining the effect of two operationalizations of variability on performance ratings: tremors (short-term changes) and swells (longer-term changes). One hundred forty-eight participants participated in a 3 (mean: below average, above average, average) × 3 (swells: positive, negative, and none) × 2 (tremors: low, high) × 2 (rater locus of control: internal, external) mixed factorial experiment. Participants evaluated 18 hypothetical salespersons’ performance distributions and made attributions about the salesperson’s locus of causality, ability, and effort. Findings indicated that both tremors and swells had a significant effect on performance ratings, such that performance profiles with a high level of tremors were rated more favorably than profiles with a low level of tremors, and profiles with a positive/negative swell were rated significantly higher/lower than profiles without a swell. As predicted, tremors had a significant effect on rater attributions of effort such that raters attributed higher amounts of effort to performance profiles with a high level of tremors compared to profiles with a low level of tremors. Swells had a significant effect on rater attributions of ability as well as attributions of effort such that raters attributed positive swells to higher levels of ability and effort and negative swells to lower levels of ability and effort. Contrary to expectation, rater locus of control did not moderate the variability performance rating relationship. However, exploratory analyses revealed that rater locus of control moderated the relationship between swells and attributions of locus of causality, such that raters with an internal locus of control tended to attribute swells internally rather than externally. Implications of these findings for performance management are discussed

The use of geometric uncertainty data in aero engine structural analysis and design

A gas turbine disc has three critical regions for which lifing calculations are essential: the assembly holes or weld areas, the hub region, and the blade-disc attachment area. Typically, a firtree joint is used to attach the blades to the turbine disc instead of a dove-tail joint, which is commonly used for compressor discs. A firtree joint involves contact between two surfaces at more than one location which makes the joint more difficult to design. Large loads generated due to the centrifugal action of the disc and associated blades are distributed over multiple areas of contact within the joint. All of the contacts in a firtree joint are required to be engaged simultaneously when the blades are loaded. However, slight variations in the manufacture of these components can have an impact on this loading. It is observed that small changes in the geometric entities representing contact between the two bodies can result in variations in the stress distribution near contact edges and the notch regions. Even though manufacturing processes have advanced considerably in the last few decades, the variations in geometry due to these processes cannot be completely eliminated. Hence, it is necessary to design such components in the presence of uncertainties in order to minimise the variation observed in their performance. In this work, the variations in geometry due to the manufacturing processes used to produce firtree joints between a gas turbine blade and the disc are evaluated. These variations are represented in two different ways using measurement data of firtree joints obtained from a coordinate measuring machine (CMM): (i) the variation for the pressure angle in the firtree joint is extracted from a simple curve fit and (ii) using the same measurement data, the unevenness of the pressure surfaces is represented using a Fourier series after filtering noise components. A parametric computer aided design (CAD) model which represents the manufacturing variability is implemented using Siemens NX. Non-smooth surfaces are also numerically generated by assuming the surface profile to be a random process. Two- and three-dimensional elastic stress analysis is carried out on the firtree joint using the finite element code, Abaqus and the variations observed in the notch stresses with changing pressure angle are extracted. A surrogate assisted multiobjective optimisation is performed on the firtree joint based on the robustness principles. Kriging based models are used to build a surrogate for notch stresses and the non-dominated sorting genetic algorithm-II (NSGA-II) is implemented to perform a multiobjective optimisation in order to minimise the mean and standard deviation of the notch stresses. An iterative search algorithm that updates the Kriging models with equally spaced infill points from the predicted Pareto front is adopted. Finally, a new design of the firtree joint is obtained which has better performance with respect to the variation in the notch stresses due to manufacturing uncertainties