在先前的研究中，特定的格點多邊形如正方形與直角三角形曾經被探討過。任意格點多邊形性質被歸類於資訊研究，目的為用程式估計當範圍很廣或邊數很多時格點多邊形性質的數值解。 先前研究中，作者已針對格點多邊形的性質進行初步的探討，本研究進一步補足先前研究的缺陷：用數學化的方式探討格點多邊形的邊數最大值。研究當中探討的多邊形包含凹多邊形及凸多邊形，研究者改良先前研究中的「迂迴作圖法」，提出新的「對稱作圖法」，以「定義基本構形、先作短邊、再作中間」的順序，確保必定可在特定範圍內建構出符合最大邊數解的格點多邊形；並以數學歸納法證明當矩形範圍短邊為12單位以上時，必存在格點數與邊數相等的格點多邊形，達成重要的突破。 本研究推導出格點多邊形的邊數最大值如下式。運用本研究的結果，將有助於在有限區域或空間中依照特定規律設計最大路徑，例如遊樂場迷宮、駕訓班車道、或積體電路設計。 S(n,m)={█(4 {if n=1∨m=1}@3n+1 {if n=2∨m=2}@24 {if m=n=4}@(n+1)(m+1) {otherwise})┤

MAGALH˜AES, Eduardo De Mˆonaco. PiezoPioggia: Energy Harvesting with Raindrops. 2024. 24 p. Research report – Scientific Apprentice Program, Col´egio Dante Alighieri, S˜ao Paulo, 2024. This project wishes to study and analyze the possibility of generating clean and accessible energy with the plain impact of droplets in the ground. Therefore, it was necessary to use piezoelectric devices in order to convert the kinetic energy of each droplet into electric energy throughout piezoelectric energy harvesting processes, (PEH). Piezoelectricity is a method of clean and sustainable energy generation, developed and explored by several scientists worldwide. Thus, while studying the proprieties of those devices, the project evaluates the present situation of electricity harvesting in Brazil, the benefits of piezoelectric technology and the possibilities it presents to economy and society. Throughout the development the project builds itself upon mathematical equations and experimental results, analyzing the deformation and generated tensions of piezos. Brand new data on the behavior of rain, as well as about the potential it presents for PEH are highlighted throughout the research, reinforcing the value of such process as a sustainable energy generation method alongside with its investment potential, both from governmental and private institutions. The project also deeply characterizes the piezoelectric device studied, diving deeply in its characteristics and evaluating the deformation of the device and treating the data sets with statistical analysis methods, in order to improve the precision of the data presented. All in all, the opportunities of piezoelectric energy harvesting in the rain, nella pioggia, shall be discussed profoundly throughout the project.

The quantum mechanical description of the four fundamental forces of nature is very important for the decryption of the rules which underlie our world. While Quantum Electrodynamics (QED) describes the electromagnetic force in great detail, it also uses complex mathematical techniques and advanced physical concepts. In the following, I will analyze to what extent a quantum mechanical two-state model can be used to describe the Coulomb interaction between two charged particles. To do so, I will exclusively focus on the electrostatic interaction, leaving dynamics aside. Furthermore, the analysis is nonrelativistic and does not consider the spin of the particles. Finally, using discrete state theory allows to explore the strength of the basic concepts of early quantum mechanics. In this sense, I will try to develop a simpli ed model for the quantum mechanical description of the electrostatic force. However, the analysis is not simplistic, since the traditional formalism of quantum mechanics will be used, including Dirac's Bra-ket notation, probability amplitudes, the Hamiltonian matrix as well as the Schrödinger equation. To understand the framework of my project, it may be helpful to take a look at the source of inspiration for my analysis: In Chapter 10 of the third volume of the well-known textbook series The Feynman Lectures on Physics[4], the force holding the hydrogen molecular ion together is explained in terms of a two-state system. The electron of the molecular ion can be either at the rst proton or at the second one. The exchange of the electron between both protons leads to an attractive force between them. It is known from QED that the electrostatic interaction between two charged particles is due to the exchange of a virtual photon which acts as force carrier. The idea of my work is to explore whether the electrostatic force can be described by a very similar model, replacing the electron acting as force carrier in the molecular ion by a virtual photon for the description of the electrostatic force between two charged particles. To describe a system consisting of charged particles, I will make the assumption that a charged particle can appear in two states. Either it is in state e where it can emit a photon or it is in state a which enables it to absorb a photon. Upon emission or absorption of a photon the charged particle transitions to the respective other state. This makes the approach analyzed in my work an element of discrete state theory, since two di erent states of the particle are used to store information about it. Of course such a model cannot be compared to the sophisticated theory of Quantum Electrodynamics. The point is, however, that it is interesting to explore the power of the most fundamental concepts of quantum mechanics and to show that such an analysis can lead to inspiring results.

Viruses Both enveloped and non-enveloped viruses conceal their membrane-penetrating peptide, usually within a glycoprotein of the virion membrane, inside the coat, or within the virion lumen. Cellular signals expose membrane-penetrating peptides that influence the virus during its entry. Instances of cellular signals regulating virus entry include receptors, enzymes, and substances like proteases, metal ions, and reducing agents. Recently, motor proteins or virus maturation have been seen to regulate virus entry through mechanical processes.

Wibrazz is a wearable communication tool that allows the teacher, the therapist, the parent to communicate information to the child remotely using the device. Haptic (vibrationbased) feedback is becoming increasingly important in everyday life. A vibrating device that transmits information through clothing can help people with disabilities who have no or limited sensory use to live an integrated life in society without barriers.

On average, the agricultural sector uses 70% of water withdrawals worldwide to produce crops1 and contributes to the eutrophication of lakes by using nutrients that are leached from the soils into lakes and reservoirs2. Vertical farming has great potential to remedy some of these issues. By growing plants vertically in controlled environments with artificial light and reusing the water, vertical farms use op to 99% less water3 and can produce up to 10 times the yield per square meter4 compared to traditional greenhouses. This improved efficiency comes at a cost; on average, vertical farms use more than 600% more energy per kilogramme of crop compared to traditional greenhouses5. 55% of this energy use is due to the use of artificial lighting6. Even though a lot of research is conducted on yield optimisation of crops in vertical farming, few research articles focus on the growth efficiency of crops to reduce the energy use in vertical farms. Only a few previous studies have tested photoperiods under 10 h·d-1. This study focuses on reducing the energy costs of light use in vertical farms by finding the photoperiod with highest energy use efficiency for the leafy vegetable arugula (eruca sativa). Energy use efficiency is defined as fresh mass per unit of electricity input (measured in kWh). In this study, arugula plants were exposed to LED growth light, with photoperiods ranging from 0 h·d-1 to 24 h·d-1 (0 h·d-1, 4 h·d-1, 7 h·d-1, 9 h·d-1, 12 h·d-1, 14 h·d-1, 16 h·d-1 and 24 h·d-1) and a PPFD of 800 μmol·m-2·s-1. The photoperiod 7 h·d-1 had the highest energy use efficiency of all photoperiods and, if used in vertical farms, this could account for approximately a 10 percent decrease in energy per kilogramme used in vertical farms (a 4 kWh decrease), with the planting density of 1400 plants per m2. This could amount to a yearly energy saving of 4,000,000 kWh per vertical farm (based on the yearly harvest of the vertical farm Nordic Harvest). This could help make vertical farming a more sustainable plant production for the future and in turn, help farming protect our water resources instead of consuming and polluting.

In the upcoming years, both population and energy consumption are expected to increase dramatically [1]. Industrialization has led to a dramatic shift in the energy environment [2], with predictions of a 57% increase in demand for energy between 2002 and 2025 [3]. In addition to organic materials like trees and solid waste, fossil fuels like coal, natural gas, and oil provide more than 90% of the world's energy needs. Their overuse has resulted in the release of climate-altering greenhouse gases like carbon dioxide (CO2) and methane (CH4) into the atmosphere [4]. Scientists and other stakeholders are putting more emphasis on finding solutions to global warming, increasing energy production in order to meet increasing demands, and decreasing emissions of greenhouse gases. Using greenhouse gasses to make useful chemicals or fuels is one solution to both problems [5]. This motivated researchers to investigate the potential of CO2 and CH4 as clean energy sources. The process of dry reforming of methane (DRM) has been identified as a potentially successful strategy for transforming CO2 into marketable syngas with a balanced H2/CO composition [6], [7], [8], [9]. The economic viability of DRM, the reactor type, the availability of raw materials, and the intended use of the produced syngas are all-important considerations. Though DRM is gaining popularity, maintaining its long-term stability is difficult due to carbon accumulation from CO disproportionation and methane degradation [10], [11]. The catalyst used, as well as other parameters like as pressure, temperature, feed concentration, and reactor size, are critical to the process's effectiveness. In this scenario, a nickel catalyst on a La2O3/SiO2 substrate with microspheres and a core-shell structure will be developed to improve the conversion of greenhouse gases into profitable syngas. This catalyst is projected to improve the efficiency and performance of the DRM process significantly.

本研究結合奈米合成技術與生物醫學， 利用表沒食子兒茶素沒食子酸酯 (Epigallocatechin gallate, EGCG) 作為載體 調控摻雜Cu2+/Cu3+與 Fe2+/Fe3+之含量 並以π-π交互作用力附載缺氧性抗癌藥物替拉扎明 (Tirapazamine, TPZ) 成功製備出多功能金屬多酚配位奈米顆粒簡稱為EFeCuTPZ。 材料經紫外-可見光譜 (UV-vis)，、動態光散射 (DLS) 及掃描式電子顯微鏡 (SEM) 確認其粒徑大小、形貌學與穩定性。利用808 nm和671 nm雷射分析其光熱轉換效率 評估光熱療法效果，。在腫瘤微酸性環境下， EFeCuTPZ可利用高濃度之H2O2行芬頓反應 (Fenton Reaction) 產生高活性之氫氧自由基 (•OH)， 展現化學動力療法 (Chemo dynamic-therapy, CDT)，。同時， 藉由材料中的Cu²⁺與腫瘤環境中的穀胱甘肽 (Glutathione, GSH)反應減少高活性物質 (Reactive oxygen species, ROS) 的消耗 增強CDT之療效。酸性條件下 TPZ顯著釋放 有助於腫瘤治療。 另外， 細胞實驗顯示EFeCuTPZ具有高生物相容性與治療效果， 成功開發出具CDT，、CT及PTT功能之奈米複合材料 為醫學新興藥物材料提供可能性。

The DIVE&CLEAN project is an educational and innovative initiative aimed at addressing a significant environmental challenge: marine pollution. With oceans covering over 70% of the Earth’s surface and providing a home to 50–80% of life on the planet, their health is critical. However, marine ecosystems are under threat due to plastic pollution, which impacts wildlife, coastal communities, and global biodiversity. This project centers around the idea of introducing underwater trash bins, especially in areas frequented by recreational divers. While most divers explore the seas without specific tools to collect trash, they could contribute significantly with the right infrastructure. The vision of DIVE&CLEAN is to inspire behavioral change, encourage collaboration, and promote actionable solutions to reduce ocean pollution. Using interactive robotics and storytelling, the project tells the story of divers rescuing animals entangled in plastic and collecting trash from the ocean floor using underwater bins. Through creative performances, it seeks to educate and motivate individuals, resorts, and authorities to adopt sustainable practices.

Road safety remains a global concern, with driver-related factors like distraction, drowsiness, and medical conditions such as stroke being leading causes of accidents. In this paper, we propose a real-time ensemble learning framework that leverages transfer learning for the detection of stroke, drowsiness, and distracted driving. Our model integrates multiple Convolutional Neural Networks (CNNs) fine-tuned for each specific task, and employs a stacking method to combine the predictions of these models using a meta-classifier. Notably, the model is optimized to enhance stroke detection, minimizing false negatives— an essential aspect for timely medical intervention. Experimental evaluations on diverse datasets demonstrate the efficacy of our approach, achieving an overall accuracy of 92.5%. The results emphasize the model’s potential for real-time driver monitoring, offering critical safety features that could reduce accidents and save lives.

The equation of an ellipse and quadratic residues are well-known concepts in elementary geometry and number theory, respectively. While the properties of ellipse equations in Euclidean space have been extensively studied, many characteristics of quadratic residues, such as consecutive quadratic residues, have also been explored in past research. In this study, we discovered the characteristic polynomial of the equation of an ellipse over finite fields Fp, a single-variable polynomial that shares the same roots as the ellipse. Furthermore, by examining the parallels between the equation of an ellipse and the pairs of residues and nonresidues, we derived a characteristic polynomial for this concept and demonstrated its connection to the Catalan number, a significant sequence in combinatorics. This research was conducted through the following steps. First, the power sums of the roots of the ellipse in Fp were calculated using the Legendre symbol and Euler’s criterion. Next, the characteristic polynomial of the ellipse was determined using Newton’s identity, generating functions, and Vieta’s theorem. Finally, leveraging the equivalence between the equation of the ellipse and the pairs of residues and nonresidues, we established the main results connecting these two concepts with Catalan numbers.

One of the main challenges with today’s batteries is their relatively low volumetric and specific capacities. The highest specific capacity can be achieved with lithium-air batteries, which use metallic lithium as the anode and typically some form of porous carbon as the cathode. To enhance performance, aerogels—among the world’s lightest solid materials—are ideal candidates for cathodes. Resorcinol-formaldehyde (RF)-based carbon aerogels, for example, serve this purpose well. In my work, I utilized two types of carbon aerogels as cathode materials: one derived from pyrolyzed resorcinol-formaldehyde polymer and the other a graphene-oxide-modified version of this carbon gel. I integrated the carbon aerogels I had pyrolyzed into lithium-air batteries to improve the cell’s performance, energy density, and capacity compared to cells using activated carbon. In my research, I examined the pore structure and surface properties of these materials in aqueous media using NMR (nuclear magnetic resonance) relaxometry and cryoporometry, exploring their impact on battery efficiency. I found that the graphene-oxide-containing sample's pores filled with water in a layered manner, indicating a more hydrophilic surface, which suggests a denser arrangement of oxygen-containing functional groups compared to the unmodified carbon aerogel. The pore sizes were reduced after adding graphene oxide, resulting in an increased specific surface area for the sample. Incorporating the reduced graphene-oxide-containing carbon aerogel enabled the creation of a more efficient, higher-capacity battery than with the RF carbon aerogel. This improved performance is likely due to the aerogel’s higher oxygen content and altered morphology. The increased oxygen content provides more active sites for oxygen reduction, meaning that a greater specific power output can be obtained from the battery.