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

Data Driven Surrogate Based Optimization in the Problem Solving Environment WBCSim

Large scale, multidisciplinary, engineering designs are always difficult due to the complexity and dimensionality of these problems. Direct coupling between the analysis codes and the optimization routines can be prohibitively time consuming due to the complexity of the underlying simulation codes. One way of tackling this problem is by constructing computationally cheap(er) approximations of the expensive simulations, that mimic the behavior of the simulation model as closely as possible. This paper presents a data driven, surrogate based optimization algorithm that uses a trust region based sequential approximate optimization (SAO) framework and a statistical sampling approach based on design of experiment (DOE) arrays. The algorithm is implemented using techniques from two packages—SURFPACK and SHEPPACK that provide a collection of approximation algorithms to build the surrogates and three different DOE techniques—full factorial (FF), Latin hypercube sampling (LHS), and central composite design (CCD)—are used to train the surrogates. The results are compared with the optimization results obtained by directly coupling an optimizer with the simulation code. The biggest concern in using the SAO framework based on statistical sampling is the generation of the required database. As the number of design variables grows, the computational cost of generating the required database grows rapidly. A data driven approach is proposed to tackle this situation, where the trick is to run the expensive simulation if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations are performed. Results show that the proposed methodology dramatically reduces the total number of calls to the expensive simulation runs during the optimization process