Multidimensional polynomial patterns over finite fields: bounds, counting estimates and Gowers norm control

We examine multidimensional polynomial progressions involving linearly independent polynomials in finite fields, proving power saving bounds for sets lacking such configurations. This jointly generalises earlier results of Peluse (for the single dimensional case) and the author (for distinct degree polynomials). In contrast to the cases studied in the aforementioned two papers, a usual PET induction argument does not give Gowers norm control over multidimensional progressions that involve polynomials of the same degrees. The main challenge is therefore to obtain Gowers norm control, and we accomplish this for all multidimensional polynomial progressions with pairwise independent polynomials. The key inputs are: (1) a quantitative version of a PET induction scheme developed in ergodic theory by Donoso, Koutsogiannis, Ferr\'e-Moragues and Sun, (2) a quantitative concatenation result for Gowers box norms in arbitrary finite abelian groups, motivated by earlier results of Tao, Ziegler, Peluse and Prendiville; (3) an adaptation to combinatorics of the box norm smoothing technique, recently developed in the ergodic setting by the author and Frantzikinakis; and (4) a new version of the multidimensional degree lowering argument

Research in advanced nuclear development and planning

Master's Project (M.S.) University of Alaska Fairbanks, 2014This project began as an examination of small and mini nuclear power plants as an emergent energy technology capable of sustained base-load power generation in northern climates. Literature review immediately demonstrated Alaska should remain current on small and mini nuclear power plants because commercial vendors are promoting their products to state leaders as certain solutions. Is Alaska prepared to receive, operate, and decommission advanced nuclear technology as an alternative to traditional hydrocarbon power plants? The graduate committee encouraged me to facilitate discussions with Alaska Center for Energy and Power (ACEP) leadership in reference to their 2010 study on small modular reactors. Gwen Holdman, Brent Sheets, and George Roe offered great encouragement for this project and allowed me to participated in nuclear related meetings with affiliates. In fall 2013, ACEP was hosting Idaho National Laboratory guests to discuss areas of common research interest. I was invited to prepare a short presentation of this project to Dr. Steven Aumeier, Director of Center for Advanced Energy Studies and Michael Hagood, Director of Program Development. ACEP and INL later determined a mobile mini reactor design for remote terrestrial deployment represents common research interests, and INL funded three UAF student fellowships at the Center for Space Nuclear Research (CSNR) Dr. Stephen Howe, Director of CSNR, allocated a team of six graduate fellows to explore terrestrial applications of a tungsten fuel matrix currently under design for nuclear thermal propulsion. UAF students selected for CSNR fellowship included Haley McIntyre, Alana Vilagi, and me. The team designed a Passively Operating Lead Arctic Reactor (POLAR), presented the POLAR design to INL staff and industry leaders and a subsequent poster was provided for the INE conference for Alaska Energy Leaders in October 2014. In addition to exceptional engineering experience, I was able to advance the graduate project in areas of technology, policy, economics, and energy infrastructure requirements needed to accept advanced nuclear technology. Concurrently, under a memorandum of agreement between the University of Alaska and Alaska Command ALCOM, I was able to advance the project to consider military applications of small modular reactors with ALCOM Energy Steering Group. It was in this context where I evaluated military installation energy usage in interior Alaska as compared to production of integral pressurized water reactors likely to emerge first in the commercial sector, and the ability of Alaska military to adopt this technology. As a side project, select courses of action were prepared and briefed to the commanding general of ALCOM should the nuclear option become attractive to the military. What began as an independent examination of small and mini nuclear power plants to satisfy a three-credit project requirement became an incredible collaboration among civilian, state, university, military, and industrial shareholders of the Alaska energy sector. Specific recognition for this report belongs to Haley McIntyre for her contribution to policy frameworks and as editor for this report, and Alana Vilagi for her contribution to process heat applications. The graduate committee along with ACEP leadership, INL-CSNR, and ALCOM should all be recognized as facilitators in this review of nuclear power in Alaska. The following report is presented in six chapters. The first two chapters attempt to introduce the reader to the current state of commercial nuclear energy in the nation as a pretext to developing the advanced reactor designs. Modifications to the existing framework are provided and the total cost of nuclear in Alaska is considered as opportunities and barriers to deployment are evaluated. As a conclusion, scenarios are developed to explain how this technology may contribute to our energy sector in the future. This project was unfunded, and its findings are intended to present a neutral examination of emergent nuclear design in the Alaska energy sector

The separation versus the cooperation of powers in the contemporary democratic state

In this paper, the authors will consider relationships between the two concepts: the separation and the cooperation of powers. At the beginning of the article various approaches to the doctrine of the separation of powers will be presented. The authors will argue that the understanding of this term must undoubtedly be reinterpreted. This is not only because the system of state organs goes beyond the classical threefold division but also due to a number of interactions emerging between state authorities. The authors will express the conviction that the concept of cooperation includes many elements of ‘positive’ influences involving a wide scope of instruments which lead to the participation of one organ in the activity of others as well as to the inspiration of one another. These cooperative instruments constitute an additional mechanism (apart from the checks and balances system) which enables to correct the mere separation

Anti-oxidant potential of plants and probiotic spp. in alleviating oxidative stress induced by H2O2

Cells produce reactive oxygen species (ROS) as a metabolic by-product. ROS molecules trigger oxidative stress as a feedback response that significantly initiates biological processes such as autophagy, apoptosis, and necrosis. Furthermore, extensive research has revealed that hydrogen peroxide (H2O2) is an important ROS entity and plays a crucial role in several physiological processes, including cell differentiation, cell signalling, and apoptosis. However, excessive production of H2O2 has been shown to disrupt biomolecules and cell organelles, leading to an inflammatory response and contributing to the development of health complications such as collagen deposition, aging, liver fibrosis, sepsis, ulcerative colitis, etc. Extracts of different plant species, phytochemicals, and Lactobacillus sp (probiotic) have been reported for their anti-oxidant potential. In this view, the researchers have gained significant interest in exploring the potential plants spp., their phytochemicals, and the potential of Lactobacillus sp. strains that exhibit anti-oxidant properties and health benefits. Thus, the current review focuses on comprehending the information related to the formation of H2O2, the factors influencing it, and their pathophysiology imposed on human health. Moreover, this review also discussed the anti-oxidant potential and role of different extract of plants, Lactobacillus sp. and their fermented products in curbing H2O2‑induced oxidative stress in both in-vitro and in-vivo models via boosting the anti-oxidative activity, inhibiting of important enzyme release and downregulation of cytochrome c, cleaved caspases-3, − 8, and − 9 expression. In particular, this knowledge will assist R&D sections in biopharmaceutical and food industries in developing herbal medicine and probiotics-based or derived food products that can effectively alleviate oxidative stress issues induced by H2O2 generation.UHK PrF Excellence project 2208/2023-2024, MH CZ - DRO (UHHK, 00179906)King Saud University Researchers Supporting Project Number (RSP2023R35) and by Scientific Grant Agency (VEGA Project 1/0482/20