This study investigates the distributional characteristics and higher-order moments of the product of multiple independent and identically distributed (i.i.d.) standard normal random variables. While the distribution of the product of two normal variables is classical, generalizing to n-fold products presents analytical and computational challenges. We derive exact expressions for higher-order moments—such as variance, skewness, and kurtosis—and demonstrate their exponential growth with dimension. A key mathematical contribution lies in the transformation of the multiplicative process via the logarithmic function, allowing the application of the Central Limit Theorem and approximation of the product as a signed log-normal variable. We also apply the Large Deviation Principle to describe rare-event probabilities of the log-product. These theoretical results are supported by a robust simulation framework that empirically validates the asymptotic behavior, highlighting how the product distribution becomes increasingly heavy-tailed and sharply concentrated near zero as n increases. Our findings offer insights into multiplicative processes and provide practical tools for applications in finance, signal processing, and neural networks. Future directions include generalization to correlated and non-Gaussian variables, and advanced tail approximations.

Upgrading fatty acid derivatives is a promising route to sustainable diesel and jet fuels, but conventional processes require high temperature, pressure, and large H₂ input, while contaminants in waste oil deactivate catalysts, demanding costly purification. Here, we present an integrated electrochemical strategy combining anodic decarboxylation, cathodic proton reduction, and olefin hydrogenation in one reactor, upgrading fatty acid derivatives to long-chain alkanes under mild conditions (60 °C, 1 atm) without external hydrogen. A high alkane yield of 88.9% is achieved and the reported performance is competitive. Experiments and calculations reveal that fatty acid chain length governs product yield and distribution by influencing -H departure and Cγ-Cβ-COOH bond cleavage barriers. This approach shows high activity and selectivity toward diverse feedstocks, including unsaturated fatty acids, esters, mixtures, crude acids, and waste oils. Powered by solar energy, approximately 40 g of long-chain alkanes are produced in a 1 L reactor, highlighting its scalability and potential for green fuel synthesis.

Alkali-activated geopolymer materials, derived predominantly from industrial byproducts such as fly ash and slag, represent a sustainable alternative to Portland cement for applications including anti-seepage grouting, road construction, and high-strength concrete. This study systematically investigates the hydration behavior of slag and fly ash activated by NaOH and Ca(OH)₂ at dosages of 4%, 6%, and 8%, with the constraint that the initial setting time is ≥ 45 min and the final setting time is ≤ 600 min. The mechanical properties of the resultant mortar systems were evaluated using standardized strength testing (ISO method) at curing ages of 3, 7, and 28 days. The phase composition and microstructural evolution of hydration products were characterized using scanning electron microscopy (SEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), backscattered electron image analysis (BSE-IA), and isothermal calorimetry. These analytical techniques provided comprehensive insights into the morphology, phase distribution, porosity, and hydration kinetics of the reaction products. The results revealed distinct activator-dependent reactivity trends: NaOH demonstrated higher efficiency in activating slag, whereas Ca(OH)₂ was more effective in promoting the hydration of fly ash. Optimal hydration was achieved with 8% NaOH for slag and 6% Ca(OH)₂ for fly ash, leading to enhanced reaction completeness, increased hydration product formation, denser pore structures, and significantly improved mechanical properties. Alkali-activated slag exhibited substantially greater strength enhancement than fly ash. The 28-day compressive strengths reached 35.94 MPa and 6.65 MPa for slag- and fly ash-based mortars, respectively, with corresponding flexural strengths of 10.23 MPa and 1.92 MPa. These findings demonstrate that the properties of alkali-activated geopolymer materials can be effectively tailored through the strategic selection of alkaline activator type and dosage. This study provides both theoretical insights and technical guidance for the development of sustainable alkali-activated geopolymer materials in construction applications.

Alkali-activated geopolymer materials, derived predominantly from industrial byproducts such as fly ash and slag, represent a sustainable alternative to Portland cement for applications including anti-seepage grouting, road construction, and high-strength concrete. This study systematically investigates the hydration behavior of slag and fly ash activated by NaOH and Ca(OH)₂ at dosages of 4%, 6%, and 8%, with the constraint that the initial setting time is ≥ 45 min and the final setting time is ≤ 600 min. The mechanical properties of the resultant mortar systems were evaluated using standardized strength testing (ISO method) at curing ages of 3, 7, and 28 days. The phase composition and microstructural evolution of hydration products were characterized using scanning electron microscopy (SEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), backscattered electron image analysis (BSE-IA), and isothermal calorimetry. These analytical techniques provided comprehensive insights into the morphology, phase distribution, porosity, and hydration kinetics of the reaction products. The results revealed distinct activator-dependent reactivity trends: NaOH demonstrated higher efficiency in activating slag, whereas Ca(OH)₂ was more effective in promoting the hydration of fly ash. Optimal hydration was achieved with 8% NaOH for slag and 6% Ca(OH)₂ for fly ash, leading to enhanced reaction completeness, increased hydration product formation, denser pore structures, and significantly improved mechanical properties. Alkali-activated slag exhibited substantially greater strength enhancement than fly ash. The 28-day compressive strengths reached 35.94 MPa and 6.65 MPa for slag- and fly ash-based mortars, respectively, with corresponding flexural strengths of 10.23 MPa and 1.92 MPa. These findings demonstrate that the properties of alkali-activated geopolymer materials can be effectively tailored through the strategic selection of alkaline activator type and dosage. This study provides both theoretical insights and technical guidance for the development of sustainable alkali-activated geopolymer materials in construction applications.

Abstract The water configuration plays a critical role in steering the CO 2 electroreduction pathway, yet achieving precise control over water arrangement remains a significant challenge. In this study, we demonstrate that introducing trace amounts of polyvinylpyrrolidone (PVP) into 3 M KCl enables targeted control over the CO 2 electroreduction product distribution by simply adjusting the PVP concentration. Using a Cu 19 CeO x (molar ratio of Cu:Ce = 19:1) electrode, in the absence of PVP, multicarbon (C 2+ ) products dominate, but substantial CO and H 2 are also generated, with negligible CH 4 formation. Remarkably, the addition of just 25 ppm PVP shifts the primary product to CH 4 , achieving a Faradaic efficiency (FE) of 60.4% at 500 mA cm −2 . Further increasing the PVP concentration to 125 ppm switches the dominant product back to C 2+ , with an impressive FE of 90.8% at 800 mA cm −2 . This trend is consistent across various Cu‐based catalysts, highlighting the universality of this approach. Mechanistic studies reveal that PVP reconstructs the water configuration at the cathode surface, modulating not only the adsorption strength and coverage of *CO intermediates but also the kinetics of water dissociation, thereby dictating the reaction pathway.

The water configuration plays a critical role in steering the CO2 electroreduction pathway, yet achieving precise control over water arrangement remains a significant challenge. In this study, we demonstrate that introducing trace amounts of polyvinylpyrrolidone (PVP) into 3M KCl enables targeted control over the CO2 electroreduction product distribution by simply adjusting the PVP concentration. Using a Cu19CeOx (molar ratio of Cu:Ce=19:1) electrode, in the absence of PVP, multicarbon (C2+) products dominate, but substantial CO and H2 are also generated, with negligible CH4 formation. Remarkably, the addition of just 25ppm PVP shifts the primary product to CH4, achieving a Faradaic efficiency (FE) of 60.4% at 500mA cm-2. Further increasing the PVP concentration to 125ppm switches the dominant product back to C2+, with an impressive FE of 90.8% at 800mA cm-2. This trend is consistent across various Cu-based catalysts, highlighting the universality of this approach. Mechanistic studies reveal that PVP reconstructs the water configuration at the cathode surface, modulating not only the adsorption strength and coverage of *CO intermediates but also the kinetics of water dissociation, thereby dictating the reaction pathway.

Study on co-pyrolysis of enzymolytic lignin and high-density polyethylene: Effects of pyrolysis parameters and synergistic interactions on the product distribution and characteristics

Mechanisms of simultaneous activation-ammoniation in co-pyrolysis of cellulose and lignin: Synergistic effects on product distribution and characteristics

Effect of torrefaction on the co-pyrolysis of pinewood with PET and HDPE: Impacts on products distribution

Bimetallic FeNi-ZSM-5-catalyzed pyrolysis of photovoltaic waste: Selective and high-yield aromatic valorization for circular resource recovery.

Microstructure regulates early-stage corrosion behavior and systemic aluminum fate in biodegradable Mg-Al alloys: Integrated in-vitro and in-vivo insights.

Conversion of cellulose to 5-hydroxymethylfurfural over vanadium-modified Dawson polyoxometalate catalysts.

High-quality, low-nitrogen bio-oil from kitchen waste via K2CO3-catalyzed solvothermal liquefaction in recycled ethanol-water co-solvent.

ABSTRACT Ambimodal transition states (TSs) lead to two or more products via post‐transition state bifurcations (PTSB). Over the past decade, numerous examples of ambimodal cycloaddition reactions have been reported, and a number of these are involved in enzyme‐catalyzed reactions in biosynthesis. This review covers enzymes known to catalyze [4 + 2]/[6 + 4] ambimodal cycloadditions, in which a single transition state leads to both [4 + 2] and [6 + 4] cycloaddition products. We also describe recent advances in computational methods for the study of bifurcations, and predictions of product ratios that are otherwise determined by calculating a large number of trajectories with quasi‐classical molecular dynamics. These methods include entropy path sampling, and product distribution predictions with correlational methods.

Temperature-dependent transformation of piggery biogas residue pyrolysis products: Balancing resource recovery and environmental safety.

Kinetic modeling of polyethylene pyrolysis under microwave irradiation toward predictive product distribution

ABSTRACT Coal pyrolysis is a pivotal process in coal utilization, including gasification, carbonization, and clean energy conversion. The pyrolysis of anthracite is fundamental in industrial production of activated carbon, and laboratory-scale synthesis of graphene and quantum dots. A thorough understanding of the molecular mechanism and kinetics of pyrolysis is critical for optimizing its utilization technologies and minimizing environmental impacts. At present, coal pyrolysis research has primarily focused on dynamic heating processes (temperature rises over time), but isothermal pyrolysis (temperature maintains constant) has received less attention. This study investigates the molecular mechanism and kinetics of isothermal pyrolysis of Taixi anthracite through a combined experimental and computational approach. Experimentally, the pyrolysis behavior of anthracite was characterized by mass loss curves and evolution of gas product distributions across varying temperatures. Reactive force field molecular dynamic (ReaxFF MD) simulation modeled the process, capturing coal consumption, gases formation, and molecular condensation, and identified the optimal temperature for maximizing energy efficiency in the simulated system. Density functional theory (DFT) calculations established a comprehensive reaction network, comprising of the initiation step and the propagation step. The results fill the knowledge gap in the fundamental understanding of coal isothermal pyrolysis and offer practical insights for optimizing the process.

The rising demand for fresh, locally sourced agricultural products, along with the need for efficient distribution approaches, has prompted interest in direct-to-consumer ecommerce models within the agriculture industry. Existing agricultural distribution systems frequently incorporate intermediaries, resulting in inefficiencies, inflated costs and delays in the delivery of perishable goods. The development of advanced technologies, including artificial intelligence (AI), has facilitated the development of more efficient, transparent, and consumer-oriented agricultural distribution systems. This paper outlines the framework of an intelligent business-to-consumer ecommerce platform for the direct distribution of agricultural products using machine learning to improve shipments, transparency and user experience. The proposed framework analyzes key factors such as price, freshness, and shipping conditions to deliver customized product recommendations and improve shipment assignment. The intelligent product recommendation and shipment assignment ensures user preference as well as the freshness of perishable goods while reducing delays and transportation expenses. Also, the proposed framework comprises of overall conceptual framework including, data collection and preprocessing steps, feature extraction, the use of recurrent neural network and singular value decomposition to train data points and evaluation metrics such as RMSA, MAE, ranking quality and cold start testing to validate intelligent model efficiency. Also, it facilitates interaction between consumers and producers, promoting a transparent, efficient, and economical distribution process. The intelligent model continuously adjusts to customer preferences and market dynamics, improving efficiency in operation and user satisfaction.

The socialization of sales improvement strategies was held at Mataram Milk, which is an micro, small and medium enterprises in the Special Region of Yogyakarta Province which focuses on the field of milk processing such as pasteurized milk with various flavors, pudding and jamu milk. This socialization aims to provide knowledge, information and strategies in order to support the increase in sales of the products, especially Mataram Milk. The problems found in Mataram Milk are regarding product marketing, production equipment and distribution permits from the Food and Drug Supervisory Agency. Mataram Milk socialization activities were carried out at the Mataram Milk business location in the Special Region of Yogyakarta with the owner of Mataram Milk through 2 (two) methods, such as observation and socialization with resource persons regarding cow's milk processing material and sales strategies for dairy products. This socialization activity provides a positive response from the owners of Mataram Milk such as interactive discussions and business owners have a clear overview for sales strategies, BPOM distribution permit requirements, milk processing production equipment.

For heavy ion radiotherapy of tumors, a persistent worldwide challenge is the inability to accurately measure the actual depth of ion beams and to assess the precision of irradiation during treatment. Positron-emitters radionuclides such as 10 C, 11 C, and 15 O, generated during the treatment process, are deposited along the beam trajectory, enabling Positron Emission Tomography (PET) imaging and the monitoring of the dose distribution primary beam. Although the distribution of positron-emitters activity can be reconstructed by a PET system, establishing a correlation between this activity and the dose is a prerequisite for employing the system to assess carbon ion beam dose distribution. In this study, a dual flat panels In-beam PET scanner was developed to investigate the relationship between the spatial activity distribution of positron products and the spatial dose distribution of carbon ions. Experiments revealed that along the Y-axis perpendicular to the beam direction, the positron activity peak shows a positional deviation of less than 0.5 mm, allowing direct beam positioning. In the beam direction, however, while the two are correlated, they do not directly coincide under the same beam energy, a millimeter-level discrepancy exists between the positron activity peak and the dose peak, and this deviation increases with higher beam energy. Based on these findings, the study proposes that a dose monitoring model using positron activity distribution as input and incorporating machine learning methods can be established, paving a new pathway for in vivo range verification and precise dose control in carbon ion therapy.