In this paper, we firstly consider extended degenerate central factorial numbers of the second kind and provide some properties of them. We then introduce unified degenerate central Bell polynomials and numbers and investigate many relations and formulas including summation formula, explicit formula and derivative property. Moreover, we derive several correlations for the fully degenerate central Bell polynomials associated with the degenerate Bernstein polynomials and the degenerate Bernoulli, Euler and Genocchi numbers.

In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion formula for the Bell polynomials in terms of the Stirling numbers of the first and second kinds, with the aid of the above explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials; (3) constructs some determinantal and product inequalities and deduces the logarithmic convexity of the Bell polynomials, with the assistance of the complete monotonicity of generating functions of the Bell polynomials. These inequalities are main results of the paper.

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

In the paper, using two inversion theorems for the Stirling numbers and binomial coecients, employing properties of the Bell polynomials of the second kind, and utilizing a higher order derivative formula for the ratio of two dierentiable functions, the authors present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, and recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit experiment is treatment of conditional probabilities corresponding to different experimental contexts as unconditional ones. Then we move to the Bell type inequalities. Bell applied classical probability theory in the same manner as Feynman and, as can be expected, he also obtained the impossibility statement. In contrast to Feynman, he formulated his no-go statement not in the probabilistic terms, but by appealing to nonlocality. This note can be considered as a part of the author's attempts for getting rid off nonlocality from quantum physics.

The emergence of Artificial Intelligence (AI) driven Keyword Spotting (KWS) technologies has revolutionized human to machine interaction. Yet, the challenge of end-to-end energy efficiency, memory footprint and system complexity of current Neural Network (NN) powered AI-KWS pipelines has remained ever present. This paper evaluates KWS utilizing a learning automata powered machine learning algorithm called the Tsetlin Machine (TM). Through significant reduction in parameter requirements and choosing logic over arithmetic based processing, the TM offers new opportunities for low-power KWS while maintaining high learning efficacy. In this paper we explore a TM based keyword spotting (KWS) pipeline to demonstrate low complexity with faster rate of convergence compared to NNs. Further, we investigate the scalability with increasing keywords and explore the potential for enabling low-power on-chip KWS.

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR) quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds. Here the coefficients involve terminating hypergeometric functions ₂F₁ and these representations are obtained by explicit computations.

Quantum Correlations are studied extensively in quantum information domain. Entanglement Measures and Quantum Discord are good examples of these actively studied correlations. Detection of violation in Bell inequalities is also a widely active area in quantum information theory world. In this work, we revisit the problem of analyzing the behavior of quantum correlations and violation of Bell inequalities in noisy channels. We extend the problem defined in [1] by observing the changes in negativity measure, quantum discord and a modified version of Horodecki measure for violation of Bell inequalities under amplitude damping, phase damping and depolarizing channels. We report different interesting results for each of these correlations and measures. All these correlations and measures decrease under decoherence channels, but some changes are very dramatical comparing to others. We investigate also separability conditions of example studied states.

The microtubule-associated protein TAU is sorted into the axon in healthy brain neurons. Somatodendritic missorting of TAU is a pathological hallmark of many neurodegenerative diseases called tauopathies, including Alzheimer’s Disease (AD). Cause, consequence, and (patho)physiological mechanisms of TAU sorting and missorting are understudied, in part also due to the lack of readily available human neuronal model systems. The human neuroblastoma cell line SH-SY5Y is widely used for studying TAU physiology and TAU-related pathology in AD and related tauopathies. SH-SY5Y cells can be differentiated into neuron-like cells (SH-SY5Y-derived neurons) using various substances. This review evaluates whether SH-SY5Y-derived neurons are a suitable model for i) investigating intracellular TAU sorting in general, and ii) with respect to neuron subtype-specific TAU vulnerability. I) SH-SY5Y-derived neurons show pronounced axodendritic polarity, high levels of axonally localized TAU protein, expression of all six major human brain isoforms, and TAU phosphorylation similar to the human brain. As proliferative cells, SH-SY5Y cells are readily accessible for genetic engineering, stable transgene integration and leading-edge genome editing are valuable and promising tools for TAU-related studies. II) Depending on the used differentiation procedure, SH-SY5Y-derived neurons resemble cells of distinct subcortical nuclei, i.e. the Locus coeruleus (LC), Nucleus basalis (NB) and Substantia nigra (SN), all of which early affected in many tauopathies. This allows to analyse neuron-specific TAU isoform expression and intracellular localization, also in the context of vulnerability to TAU pathology. Limitations are e.g. the lack of mimicking age-related tauopathy risk factors and the difficulty to define the exact neuronal subtype of SH-SY5Y-derived neurons. In brief, this review discusses the suitability of SH-SY5Y-derived neurons for investigating TAU (mis)sorting mechanisms and neuron-specific TAU vulnerability in disease paradigms.

Sequential properties can violate Bell-type inequalities without direct influence on each other, but only if detected in pairs. This is demonstrated below with theoretical arguments, and with a straightforward toy model. Rotating arrows can have transient qualities that produce maximal Bell violations with predetermined values. Any non-signaling phenomenon (classical, or non-classical) can also be interpreted as local.

This paper is concerned with representing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials which involve the hypergeometric functions ${}_1 F_1$ and ${}_2 F_1$.

This paper presents an advanced software tool for precise laser beam propagation analysis, focusing on the calculation of the M2 value, a key measure of beam quality. Developed in Python, the software integrates libraries like NumPy, Matplotlib, and SciPy for robust data handling and accurate polynomial fitting. It features a user-friendly interface for easy data input, analysis, and visualization, making it accessible to both professionals and novices. The tool has been rigorously validated against theoretical models (M2=1) and experimental data (showing M2=1.2548 and 1.3166), ensuring high accuracy and reliability. It visualizes beam width data and fitted polynomial curves, aiding in assessing beam propagation characteristics and optimizing laser systems. Future enhancements include additional beam quality metrics, machine learning integration, and cloud-based functionality. This tool significantly advances laser beam analysis, benefiting research and industrial applications by improving performance and efficiency. The software is available at DOI: 10.5281/zenodo.13325911

Nutraceuticals comprise dietary supplements, functional foods, medicinal foods, and pharmaceuticals. However, to date all these concepts are interpreted in different ways with the rapid increasing knowledge on nutrition, medicine, and plant biotechnology changing the concepts about food, health and agriculture. What matters are the bioactive elements conveyed by foodstuffs as nutrients or non-nutrients, which interfere with human metabolism and have impact on health, aging and well-being. Food, not nutrients, is the fundamental unit in nutrition and edible mushrooms, are fungi that supply unique biological compounds, different from plant or animal origin, which significantly impact on health status. Their influence on medicinal interventions has been known and studied for many years. The role on neurodegenerative disorders has been recently investigated and their significance on many other diseases has been well demonstrated. On this note it is synthesized the more recent knowledge of some edible mushrooms and preparations on Ménière’s disease, a lifelong condition it can develop at any age, but most commonly appearing between 40 and 60 years of age.

We describe results from a Monte-Carlo simulation of Bell-CHSH type correlations in hydrodynamic walkers. We study feasibility of a real life walker test with relevant hydrodynamic parametric ranges. We observe the generic formation of pairs of walkers strongly anti-correlated both in position and momentum. With this source of entangled walkers, we model the insertion of 2 pins in the bath as a notion of measure, akin to the polarizers of photonic Bell tests. This insertion of pins, either static or dynamic, introduces 2 weak field signals. Each field has the physical form of a standing wave Bessel hat, representing the non-local (field mediated) influences of the measure on the walkers. With this representation of the measure, we develop protocol for a Bell game with actual hydrodynamic walkers. We model both static and dynamic insertion of pins in the walker bath. Static pins give us numerical S > 2, as a permissible Bell violation for a non-local (field based) effect. Dynamic insertion of the pins, however, leads to causal space separation of the two arms. We observe the again expected S ≤ 2. We argue for the hydrodynamic implementation and observation of these effects as a walker visualization of Bell inequalities.

The integration of solar energy systems with agricultural practices, known as agrivoltaic systems, presents a promising solution for advancing sustainable food and energy production. This approach involves installing photovoltaic panels on agricultural lands, which allows for simultaneous crop cultivation and energy generation. Agrivoltaic systems offer a dual benefit: they enhance land use efficiency by utilizing the same area for both solar power generation and crop production, and they contribute to sustainable energy transitions. This abstract explores the benefits and challenges associated with agrivoltaic systems. Key advantages include increased land productivity, reduction in water usage due to shading effects, and potential economic gains from dual income streams. Furthermore, these systems can mitigate land use conflicts by combining food production with renewable energy generation. However, there are challenges to address, including the potential for decreased crop yields under solar panels, the need for appropriate system design to balance energy generation and agricultural needs, and the economic feasibility of initial investment and maintenance. The integration of agrivoltaic systems represents a critical step toward achieving sustainable development goals by promoting environmental stewardship and resource efficiency. Future research and advancements in technology are essential to optimize system performance and maximize benefits for both agriculture and energy sectors.

It is becoming clear that in addition to gap junctions, playing a role in cell-cell communication, gap junction proteins, connexins, located in cytoplasmic-compartments may have other important functions. Mitochondrial connexin 43 (Cx43) is increased after ischemic preconditioning and has been suggested to play a protective role in the heart. How Cx43 traffics to the mitochondria and the interactions of mitochondria with other Cx43-containing structures are unknown. In this study, immunocytochemical, super-resolution and transmission electron microscopy were used to detect cytoplasmic Cx43-containing structure and to demonstrate their interactions with other cytoplasmic organelles. The most prominent cytoplasmic Cx43-containing structures, annular gap junctions, were demonstrated to form intimate associations with lysosomes as well as with mitochondria. Surprisingly, the frequency of associations between mitochondria and annular gap junctions was greater than that between lysosomes and annular gap junctions. The benefits of annular gap junction/mitochondrial associations are not known. However, it is tempting to suggest that the contact between annular gap junction vesicles and mitochondria facilitates Cx43 deliver to the mitochondria. Furthermore, it points to the need for investigating trafficking of Cx43 to cytoplasmic compartments and annular gap junction as more than only a vesicle destined for degradation.

When profit-driven renewal is difficult to implement, many historic districts are “frozen protected” in China. In the social context of “building cities for the people” in recent years, the public value-oriented renewal of urban historic areas plays an important role in the transformation of cities. This study investigates the strategies of historic district regeneration in China by integrating spatial form, urban governance, and public value. We propose a novel framework to analyze the regeneration of historic districts, using Taiyuan Bell Tower Street as a case study. The framework distinguishes between two dimensions: spatial and economic-social. In the spatial dimension, we focus on the transformation of spatial form to regenerate public value, emphasizing the attribute of "publicness" as central to urban regeneration efforts. This involves a tiered approach of excavating and upgrading historic districts at macro, meso, and micro levels. In the economic-social dimension, we explore urban governance to strengthen public value, involving government, market, and societal actors in a collaborative renewal process. The analysis highlights that a public value-oriented approach to heritage regeneration offers greater sustainability and could serve as a model for other cities seeking similar outcomes.

Influencer marketing has become a pivotal component of digital marketing strategies, offering brands a unique way to connect with audiences through trusted voices. However, measuring the return on investment (ROI) from influencer marketing campaigns can be challenging due to the intangible nature of brand influence and engagement. This abstract explores various techniques and strategies to measure and optimize ROI in influencer marketing. Measurement Techniques: The paper delves into both quantitative and qualitative methods for assessing influencer marketing ROI. Quantitative techniques include tracking metrics such as impressions, clicks, conversions, and sales, using tools like Google Analytics and social media insights. Additionally, advanced attribution models, such as multi-touch attribution and econometric modeling, are discussed for more accurately linking influencer activities to business outcomes. Qualitative approaches involve sentiment analysis and brand awareness studies, which help gauge the impact of campaigns on brand perception and customer loyalty. Optimization Strategies: To maximize the effectiveness of influencer marketing, the paper outlines several optimization strategies. These include selecting the right influencers based on audience alignment and engagement rates, setting clear and measurable campaign goals, and employing A/B testing to refine content and strategies. The importance of long-term partnerships and content diversification is also emphasized, as they can enhance authenticity and sustain audience interest. The abstract concludes that a comprehensive approach combining rigorous measurement techniques and strategic optimization can significantly enhance the ROI of influencer marketing campaigns. By continuously analyzing data and refining strategies, brands can better leverage influencer partnerships to achieve their marketing objectives.

The convergence of digital twin technology with additive manufacturing (AM) represents a transformative advancement in the fields of design, simulation, and production. Digital twins—virtual replicas of physical assets—enable real-time monitoring, simulation, and optimization of manufacturing processes by mirroring their physical counterparts. When integrated with additive manufacturing, which allows for the creation of complex geometries and rapid prototyping, digital twins enhance the ability to design, test, and refine products with unprecedented precision and efficiency. This integration facilitates iterative design improvements, predictive maintenance, and real-time process adjustments, leading to more accurate simulations and optimized production workflows. By leveraging data from digital twins, manufacturers can anticipate issues, reduce material waste, and shorten development cycles. This abstract explores how the fusion of digital twin technology with AM not only refines traditional manufacturing paradigms but also paves the way for more innovative and adaptive manufacturing practices.

The advent of artificial intelligence (AI) has revolutionized digital marketing, offering unprecedented levels of personalization. AI-driven personalization leverages machine learning algorithms and data analytics to tailor content, advertisements, and recommendations to individual consumers based on their behavior, preferences, and demographics. This paper explores the effectiveness of AI-driven personalization in enhancing customer engagement, increasing conversion rates, and improving overall marketing efficiency. It also examines the ethical considerations associated with these technologies, including data privacy, consent, and the potential for manipulation or bias. While AI-driven personalization can lead to more relevant and engaging consumer experiences, it raises critical ethical questions that must be addressed to ensure responsible and fair use. The study concludes with recommendations for marketers and policymakers to balance the benefits of AI personalization with the need for ethical standards and consumer protection.

Perovskite-silicon tandem solar cells represent a significant advancement in photovoltaic technology, aiming to overcome the efficiency limitations of traditional silicon-based solar cells. This paper explores recent developments in the fabrication and optimization of these tandem cells, focusing on improving both efficiency and long-term stability. The combination of perovskite materials with silicon allows for broader spectrum absorption, which enhances the overall power conversion efficiency. Key strategies include optimizing the perovskite layer's composition, improving the interface between layers to reduce recombination losses, and incorporating advanced encapsulation techniques to mitigate degradation from environmental factors such as moisture and UV exposure. The review also highlights the challenges faced in scaling up production while maintaining high performance and stability. Emerging trends in material engineering and device architecture are discussed, providing insights into future directions for making perovskite-silicon tandem solar cells a viable commercial technology. This study underscores the potential of these hybrid systems to significantly boost the efficiency of photovoltaic systems, offering a promising pathway towards more sustainable and costeffective solar energy solutions.

There is a growing demand for indoor positioning systems (IPS) in a wide range of applications. However, traditional solutions such as GPS face many technical challenges. In recent years, a promising alternative has been emerging: IPS based on visible light communication (VLC), which offers a combination of which is highly accurate, low cost and energy efficient. This article presents a comprehensive review of VLC-based IPS, providing a tutorial-like overview of the system. It begins by comparing various positioning systems and providing background information on their inherent limitations. The mechanisms of VLC-based IPS are then discussed, including a comprehensive examination of their performance metrics and underlying assumptions. The complexity and efficiency of VLC-based IPS is examined by analyzing factors such as channel modeling, signal processing, and localization algorithms. To optimize the system, a variety of strategies are explored. These include the design of efficient modulation schemes, the development of advanced encoding and decoding algorithms, the implementation of adaptive power control, and the use of state-of-the-art localization algorithms. Additionally, system parameters such as LED placement, receiver sensitivity, and transmit power are carefully examined to highlight their impact on energy efficiency and localization accuracy. Altogether, this paper serves as a comprehensive guide to VLC IPS, providing in-depth insights into its vast potential and the challenges it presents.

The transition to renewable energy sources is critical for sustainable development, particularly in rural regions with limited access to electricity. Solar-powered microgrids offer a promising solution for rural electrification by providing reliable, clean energy that can enhance economic opportunities and improve quality of life. This paper presents a techno-economic analysis of solar-powered microgrids for rural areas, evaluating their feasibility, costs, and benefits. The analysis encompasses technological aspects, such as solar panel efficiency, battery storage, and grid management, alongside economic factors including initial investment, maintenance costs, and potential returns. Additionally, the study assesses the social impact of solar-powered microgrids, exploring their effects on local communities, including improvements in education, health, and economic activities. The findings indicate that solar microgrids can be a viable and impactful solution for rural electrification, with significant long-term benefits for both economic development and social well-being.

Here we consider sums of finite products of Chebyshev polynomials of the third and fourth kinds. Then we represent each of those sums of finite products as linear combinations of the four kinds of Chebyshev polynomials which involve the hypergeometric function ₃F₂.

4D printing represents an innovative evolution of 3D printing technologies, incorporating time as a fourth dimension to create objects that can transform and adapt over time in response to environmental stimuli. This emerging field has shown significant advancements in materials science, design principles, and applications. Recent research focuses on developing responsive materials such as shape-memory polymers, hydrogels, and composites that can undergo controlled transformations in reaction to changes in temperature, humidity, or other external factors. The advancements in 4D printing have led to a wide array of applications, including self-healing structures, adaptive medical devices, and dynamic architectural components. This abstract examines the latest progress in 4D printing technologies, highlighting key advancements in material development and design strategies. It explores various case studies that demonstrate the practical implementation of 4D-printed objects across different sectors. Furthermore, the abstract discusses the challenges faced by researchers, including material limitations, scalability issues, and the need for standardized testing methods. The potential future directions of 4D printing are also considered, emphasizing the need for interdisciplinary collaboration to overcome current limitations and expand the range of applications. This research underscores the transformative potential of 4D printing in creating intelligent and adaptable systems, offering significant benefits across industries from healthcare to construction.

Metal additive manufacturing (AM), commonly referred to as 3D printing with metals, is an innovative technology with significant potential to transform industries such as aerospace, automotive, and healthcare. Despite its promise, the field faces several challenges that impact both its technical feasibility and economic viability. This paper explores the primary technical challenges, including material properties and processing complexities, such as the need for precise control of thermal gradients and the mitigation of defects like porosity and residual stresses. Additionally, it addresses the economic barriers, including high initial equipment costs, the need for specialized knowledge, and the relatively slow build speeds compared to traditional manufacturing methods. By examining these challenges, this paper aims to provide a comprehensive overview of the current state of metal additive manufacturing and suggest potential pathways for overcoming these obstacles to facilitate wider adoption and technological advancement in the field.

This study examines change detection techniques in dense point clouds for the purpose of Cultural Heritage preservation, with a particular focus on the San Pietro Barisano Bell Tower in Matera, Italy. Dense point clouds, obtained via advanced laser scanning, offer detailed 3D representations of heritage structures, facilitating the precise monitoring changes over time. The investigation uses a variety of change detection algorithms, including the Iterative Closest Point (ICP) algorithm, which is renowned for its robust registration capabilities in aligning point clouds with high accuracy. The combination of ICP with deviation analysis and feature-based methods allows for the effective identification of alterations, including deformations, material loss, and surface degradation. This methodology establishes a comprehensive framework for the monitoring of Cultural Heritage, thereby enabling timely and targeted preservation efforts. The results emphasise the substantial contribution of dense point cloud analysis to the enhancement of heritage management and the safeguarding of vulnerable architectural sites.

Although mammography has been the gold standard for early detection of breast cancer, if a woman has dense breast tissue, a false negative diagnosis may occur. Breast ultrasound, whether hand-held or automated, is a useful adjunct to mammography but adds extra time and cost. The primary aim was to demonstrate that our second-generation Aceso system, which combines full-field digital mammography (FFDM) and automated breast ultrasound (ABUS) in a single platform, is able to produce improved quality images that provide clinically meaningful results. Aceso was first tested using two industry standards: a CDMAM phantom to assess the FFDM images; and the CIRS 054GS phantom to evaluate the ABUS images. In addition, 25 women participated in a clinical trial: 14 were healthy volunteers while 11 were patients referred by the breast clinic at Groote Schuur Hospital. The CDMAM phantom results showed the FFDM results were better than EUREF’s standard of “acceptable” and were approaching “achievable”. The ABUS results showed lateral and axial spatial resolution of 0.5 mm and adequate depth penetration of 80 mm. Our second-generation Aceso system, with its improved quality of clinical FFDM and ABUS images, has demonstrated its potential for early detection of breast cancer in a busy clinic.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

Quantum theory predicts a whole class of non-local phenomena, observable via coincident detection of EPR-type systems. An important feature of these observations is their non-signaling character. Technically, non-local phenomena should only be observable for post-selected sub-ensembles, rather than for complete projections. Otherwise, superluminal telegraphy becomes possible. Yet, a couple of recent Bell experiments reported the observation of quantum non-locality for 100% of the detected events. Does it follow that signaling non-locality is possible? If so, was quantum theory falsified? This puzzle is solved by revisiting the interpretation of the spin projection operator, with special focus on its dual nature (combining spectral decomposition with spectral transformation). “Component switching” is not a loophole, but rather a requirement of quantum mechanics in this context, because sharp spin projections are partial (as well as partially overlapping). Surprisingly, it is possible to pre-select incompatible statistical sub-ensembles with heralded detection and to reveal the same behavior as in post-selected observations. Therefore, Bell experiments confirm the predictions of quantum theory without violating the non-signaling principle.

We show that the respective oversights in the von Neumann's general theorem against all hidden variable theories and Bell's theorem against their local-realistic counterparts are homologous. Both theorems unjustifiably assume the additivity of expectation values within hidden variable theories to derive their respective conclusions. However, for non-commuting observables, the equivalence of a sum of expectation values and the expectation value of the sum of measurement results, although respected within quantum mechanics, need not hold for hidden variable theories, regardless of specific characteristics such as local realism they may respect. Once this oversight is ameliorated from Bell's argument and local realism is implemented correctly, the bounds on the CHSH correlator work out to be +/-2\/2 instead of +/-2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values.

The COVID-19 pandemic has had devastating consequences for health, social, and economic domains, but what has received far less focus is the effect on people’s relationship to vital ecological supports, including access to greenspace. We assessed patterns of greenspace use in relation to individual and environmental factors and their relationship with experiencing psychological symptoms under the pandemic. We conducted an online survey recruiting participants from social media for adults in Korea for September–December 2020. The survey collected data on demographics, patterns of using greenspace during the pandemic, and major depression (MD) and generalized anxiety disorder (GAD) symptoms. The Patient Health Questionnaire (PHQ-9) and the Generalized Anxiety Disorder 2-item (GAD-2) were applied to identify probable cases of MD and GAD. A logistic regression model assessed the association decreased visits to greenspace after the outbreak compared to 2019 and probable MD and GAD. Among the 322 survey participants, prevalence of probable MD and GAD were 19.3% and 14.9%, respectively. High rates of probable MD (23.3%) and GAD (19.4%) were found among persons currently having job-related and financial issues. Of the total participants, 64.9% reported decreased visits to greenspace after the COVID-19 outbreak. Persons with decreased visits to greenspace had 2.06 higher odds (95% CI: 0.91, 4.67) of probable MD at the time of the survey than persons whose visits to greenspace increased or did not change. Findings suggest that barriers to greenspace use could deprive people of mental health benefits and affect mental health during pandemic; an alternative explanation is that those experiencing poor mental health may be less likely to visit greenspaces during pandemic. This implies the need of adequate interventions on greenspace uses under an outbreak especially focusing on how low-income populations may be more adversely affected by a pandemic and its policy responses.

In the paper, by a very simple approach, the author establishes an expression in terms of a lower Hessenberg determinant for the Euler polynomials. By the determinantal expression, the author finds a recurrence relation for the Euler polynomials. By the way, the author derives the corresponding expression and recurrence relation for the Euler numbers.

Coastal inundation is an increasing problem. Sea-level rise will greatly increase the frequency and depth of inundation, forcing vulnerable communities to adapt. Communities will need to decide when and how to adapt. The process of decision-making along adaptive pathways is now being used internationally to plan for adaptation over time by anticipating decision points in the future however it unfolds. This process requires risk and uncertainty considerations to be transparent in the scenarios used in such planning. We outline a framework for uncertainty identification and management within coastal hazard assessments which recognizes different types of decision and identifies the types of uncertainty that must be accounted for, such as statistical, scenario and deep uncertainty types. We show how coastal-inundation hazard can be mapped and presented in a way that clearly separates sources of uncertainty, so that they are transparent within a dynamic adaptive pathways planning process. Traditional coastal inundation maps show inundated area only. We present maps of inundation depth and frequency which clearly show the degree of exposure, where that exposure occurs, and how much sea-level rise can be tolerated. The new uncertainty framework and mapping techniques can better identify decision points and their expected time range, which provides more useful input to the adaptation process than traditional coastal inundation assessments.

Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.

In this paper, we represent the generating function of w-torsion Fubini polynomials by fermionic p-adic integral on Z_p. Then we consider a quotient of such fermionic p-adic integrals on Z_p, representing generating functions of three w-torsion Fubini polynomials and derive some new symmetric identities for the w-torsion Fubini and two variable w-torsion Fubini polynomials.

The microbioma is presently one of the hottest areas of scientific and medical research and exerts a marked influence on the host during homeostasis and disease. Fermented foods arise in the human relationship to the microbial environment. Further to the traditionally recognized effects of fermented foods and beverages on the digestive health and well-being there is now strong evidence on their general health benefits, namely the significance on the gut microbiota and brain functionality. We highlight the possibilities in this field, how little is still known, and call for a convergence of interdisciplinary research fields of One Health microbe-nutrition with fermented foods and gut-brain research. A consequence of civilisation, changes in present-day society in diets with more sugar, fat and salt, habits and lifestyle, contributes to the likelihood of an inflammatory microbiome, particularly the global epidemics of obesity and mental health. Although two recent papers claim that probiotics perturb rather than aid in microbiota recovery back to baseline after antibiotic administration in humans, consuming fermented foods has shown to reduce inflammation so improve gut health and the proper function of the body’s immune system.

In this paper, we introduce the partially degenerate Changhee-Genocchi polynomials and numbers and investigated some identities of these polynomials. Furthermore, we investigate some explicit identities and properties of the partially degenerate Changhee-Genocchi arising from the nonlinear dierential equations.

Quantum Correlations are studied extensively in quantum information domain. Entanglement Measures and Quantum Discord are good examples of these actively studied correlations. Detection of violation in Bell inequalities is also a widely active area in quantum information theory world. In this work, we revisit the problem of analyzing the behavior of quantum correlations and violation of Bell inequalities in noisy channels. We extend the problem defined in a recent study by observing the changes in negativity measure, quantum discord and a modified version of Horodecki measure for violation of Bell inequalities under amplitude damping, phase damping and depolarizing channels. We report different interesting results for each of these correlations and measures. All these correlations and measures decrease under decoherence channels, but some changes are very dramatical comparing to others. We investigate also separability conditions of example studied states.

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

Sustainability in Additive Manufacturing (AM) is an emerging area of research that examines the environmental impacts and potential benefits of AM processes compared to traditional manufacturing methods. This paper analyzes the environmental footprint of additive manufacturing technologies, including material usage, energy consumption, and waste production. AM techniques, such as fused deposition modeling (FDM), stereolithography (SLA), and selective laser sintering (SLS), are evaluated for their efficiency and sustainability. Key factors such as resource utilization, lifecycle emissions, and recyclability are assessed to determine how AM can contribute to a more sustainable manufacturing paradigm. The study highlights that while AM offers advantages such as reduced material waste and the potential for localized production, it also poses challenges, including high energy consumption and limited material options. The paper concludes with recommendations for improving the environmental performance of AM, including advancements in material science, energy-efficient technologies, and the integration of circular economy principles. By addressing these aspects, AM can play a significant role in achieving sustainability goals in manufacturing.

Additive manufacturing (AM), commonly known as 3D printing, has revolutionized the production of complex geometries that were once challenging or impossible to achieve through traditional manufacturing techniques. This paper investigates the capabilities of additive manufacturing in producing intricate designs, focusing on the unique advantages and potential applications across various industries. Additive manufacturing enables the creation of complex geometries by adding material layer by layer, allowing for greater design freedom and the ability to produce structures with intricate internal features, complex curves, and lightweight lattice structures. This capability is particularly advantageous in fields such as aerospace, biomedical, and automotive, where weight reduction, customization, and the integration of complex internal channels are critical. The study explores various additive manufacturing technologies, including stereolithography (SLA), selective laser sintering (SLS), and fused deposition modeling (FDM), highlighting their specific strengths and limitations in producing complex geometries. Factors such as material properties, resolution, surface finish, and build size are analyzed to determine the suitability of different AM processes for specific applications. Additionally, the research delves into the design considerations and software tools that facilitate the creation of complex geometries in AM, including generative design and topology optimization. These tools leverage the design freedom offered by AM to optimize structures for weight, strength, and functionality, pushing the boundaries of what is possible in product design. The paper concludes with an examination of the challenges and future directions in the field, such as improving material properties, reducing production costs, and enhancing the accuracy and reliability of AM processes. The potential of additive manufacturing to revolutionize the production of complex geometries is underscored, emphasizing its growing importance in modern manufacturing and its role in enabling innovative solutions across various industries. This abstract provides an overview of the potential and challenges of additive manufacturing for producing complex geometries, suitable for an academic paper or report. If you need more specific information or have a different focus, feel free to ask!

Additive Manufacturing (AM), commonly known as 3D printing, has revolutionized various industries, including the medical field. This technology enables the creation of complex structures layer by layer, offering unprecedented customization and precision. In medical applications, AM has proven transformative in producing patient-specific implants, prosthetics, and anatomical models, facilitating better surgical planning and outcomes. Additionally, it has shown promise in bioprinting, where cells and biomaterials are used to create tissue-like structures for regenerative medicine. The ability to rapidly prototype and manufacture medical devices reduces time and costs, and enhances personalized patient care. This abstract explores the diverse applications, benefits, and challenges of AM in the medical sector, highlighting its potential to revolutionize healthcare and improve patient outcomes.

In the digital age, social media platforms have become a critical channel for brands to engage with their audience and manage their reputation. This paper explores the application of sentiment analysis in social media to aid brand reputation management. Sentiment analysis, a subset of natural language processing (NLP), involves determining the emotional tone behind online discussions and opinions. By leveraging machine learning algorithms and NLP techniques, brands can analyze vast amounts of social media data to gauge public sentiment, identify emerging trends, and detect potential issues before they escalate. This study reviews current methodologies in sentiment analysis, including supervised and unsupervised learning approaches, and discusses their effectiveness in extracting actionable insights from social media content. Additionally, it examines case studies where sentiment analysis has been successfully implemented to enhance brand reputation, address customer concerns, and tailor marketing strategies. The findings highlight the importance of continuous monitoring and adaptation to dynamic social media landscapes for maintaining a positive brand image. This paper provides a comprehensive overview of sentiment analysis tools and techniques, offering practical recommendations for brands seeking to leverage social media sentiment data for proactive reputation management.

In the evolving landscape of digital marketing, cross-channel attribution modeling plays a crucial role in understanding and optimizing the customer journey across various touchpoints. As consumers interact with brands through multiple channels—such as social media, email, search engines, and display ads—accurately attributing conversions to the right channels is vital for optimizing marketing strategies and budgets. However, the advent of stringent privacy regulations, such as the General Data Protection Regulation (GDPR) and the California Consumer Privacy Act (CCPA), has significantly impacted the data collection and analysis processes in digital marketing. This paper explores the challenges and opportunities presented by cross-channel attribution modeling in the age of heightened privacy awareness. It examines how traditional data-driven attribution models, which often rely on tracking individual user behavior, are being adapted or replaced in response to privacy concerns and regulatory requirements. The paper discusses the emergence of privacy-preserving techniques, such as aggregated data analysis, differential privacy, and the use of anonymized data, which aim to balance the need for accurate attribution with the protection of consumer privacy. Furthermore, the paper highlights the role of first-party data and the growing importance of consent management in the collection and utilization of consumer information. It also investigates how marketers are leveraging advancements in artificial intelligence and machine learning to enhance attribution models in a privacy-conscious world. The study concludes by offering best practices for businesses seeking to navigate the complexities of cross-channel attribution in the context of evolving privacy regulations, emphasizing the need for transparency, compliance, and ethical data handling. This research provides valuable insights for marketers, data scientists, and policymakers on how to effectively manage the interplay between accurate attribution and privacy, ensuring that marketing efforts remain effective while respecting consumer rights.

The field of polymer additive manufacturing (AM) has experienced rapid evolution, marked by significant advancements in materials science and technology. This paper reviews recent innovations in polymer materials tailored for additive manufacturing processes, focusing on enhancements in mechanical properties, functionalization, and processability. Key developments include the introduction of high-performance thermoplastics, composite materials incorporating fibers or nanoparticles, and novel photocurable resins. These materials offer improved strength, durability, and versatility compared to traditional polymers. Furthermore, research into bio-based and recyclable polymers highlights a growing trend towards sustainable manufacturing practices. Advances in material formulations, including self-healing and shape-memory polymers, are also examined for their potential to transform applications across various industries. This review synthesizes current research trends and provides a comprehensive overview of the state-of-the-art in polymer AM materials, emphasizing the impact of these innovations on the future of manufacturing technologies.

Additive manufacturing (AM), commonly known as 3D printing, has emerged as a transformative technology in supply chain management (SCM). This abstract explores how AM influences various aspects of SCM, including inventory management, production processes, and logistics. By enabling on-demand production and reducing reliance on traditional manufacturing methods, AM minimizes inventory costs and enhances customization capabilities. It also facilitates localized production, which can reduce lead times and transportation costs. The integration of AM into SCM fosters greater flexibility and resilience, allowing businesses to respond more swiftly to market changes and disruptions. This study highlights both the opportunities and challenges associated with adopting AM, emphasizing the need for strategic adjustments to fully leverage its potential in modern supply chains.

The integration of additive manufacturing (AM), commonly known as 3D printing, has revolutionized aerospace engineering by enabling the creation of complex, lightweight, and high-performance components. This paper explores the transformative impact of AM technologies on the design, production, and maintenance of aerospace systems. The aerospace industry demands high precision, reduced weight, and enhanced performance, all of which are facilitated by AM's ability to produce intricate geometries and optimize material usage. Key applications of AM in aerospace include the fabrication of engine components, structural parts, and customized tooling. The technology's capability to produce parts with complex internal structures, such as lattice designs, leads to significant weight reductions without compromising strength and durability. Furthermore, AM allows for rapid prototyping, enabling faster iteration and development cycles, which is crucial in the highly competitive aerospace sector.

The advancement of high-temperature structural materials is crucial for the efficiency and performance of modern gas turbines, which are widely used in aviation and power generation. This paper explores the development and optimization of materials capable of withstanding extreme temperatures, mechanical stresses, and corrosive environments within turbine engines. The focus is on nickel-based superalloys, ceramic matrix composites (CMCs), and emerging materials such as high entropy alloys (HEAs) and refractory metals. Nickel-based superalloys are the current standard due to their excellent high-temperature strength and creep resistance, while CMCs offer potential for weight reduction and improved thermal efficiency. High entropy alloys, characterized by their unique multi-component systems, present promising properties including high strength and oxidation resistance at elevated temperatures. Additionally, advances in coating technologies and additive manufacturing are enhancing the durability and performance of these materials. The paper also discusses the challenges associated with material development, including the trade-off between strength and ductility, manufacturing complexities, and the need for long-term performance data. Future research directions are identified, focusing on the integration of computational materials science and advanced characterization techniques to accelerate the discovery and implementation of next-generation high-temperature materials. The successful development of these materials is essential for improving the efficiency and reducing the environmental impact of gas turbines.

We use a recently proposed formulation of quantum mechanics based, not on potential functions but rather, on orthogonal energy polynomials. In this context, the most important building block of a quantum mechanical system, which is the wavefunction at a given energy, is expressed as pointwise convergent series of square integrable functions in configuration space. The expansion coefficients of the series are orthogonal polynomials in the energy; they contain all physical information about the system. No reference is made at all to the usual potential function. We consider, in this new formulation, few representative problems at the level of undergraduate students who took at least two courses in quantum mechanics and are familiar with the basics of orthogonal polynomials. The objective is to demonstrate the viability of this formulation of quantum mechanics and its power in generating rich energy spectra illustrating the physical significance of these energy polynomials in the description of a quantum system. To assist students, partial solutions are given in an appendix as tables and figures.

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. One of these is a four-parameter polynomial with a discrete spectrum. Another that appeared while solving a Heun-type equation has a mix of continuous and discrete spectra. Based on these results and on our recent study of the solution space of an ordinary differential equation of the second kind with four singular points, we introduce a modification of the hypergeometric polynomials in the Askey scheme. Up to now, all of these polynomials are defined only by their three-term recursion relations and initial values. However, their other properties like the weight function, generating function, orthogonality, Rodrigues-type formula, etc. are yet to be derived analytically. This is an open problem in orthogonal polynomials.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

In this article, the Legendre-Gould Hopper polynomials are combined with Sheffer sequences to introduce certain mixed type special polynomials. Generating functions, differential equations and certain other properties of Legendre-Gould Hopper based Sheffer polynomials are derived. Further, operational and integral representations providing connections between these polynomials and known special polynomials are established. Certain identities and results for some members of these new mixed polynomials are also obtained. Finally, the determinantal definitions of Legendre-Gould Hopper based Sheffer polynomials are also given.

In this paper, we introduce a new class of degenerate Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of degenerate Hermite-Fubini numbers and polynomials by using generating functions.

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers. Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

In this paper, we investigate the recently introduced degenerate Bernstein polynomials and operators and derive some of their properties. Also, we give some properties of the degenerate Euler numbers and polynomials and their connection with the degenerate Euler polynomials.

In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].

The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. The measurements made on the photons shows that light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement. Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. It was found that violation of Bell's inequalities could be trivially calculated and for sets of nonmaximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we visit violation of Bell's inequalities problem with a different approach. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with violation in Bell's inequalities and we make similar comparison of this violation with commonly studied entanglement measures, negativity and relative entropy of entanglement. We show that there are interesting orderings for system states.

In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the Stirling polynomials in terms of the Stirling numbers of the first and second kinds.

Frequent flooding from sea-level rise (SLR) is one of the immediate climate change impacts affecting low-lying and exposed coastal communities. These communities rely upon the delivery of three-waters services for wastewater, stormwater and water supply. Due to ongoing SLR, managing these networks will increasingly be a challenge. This raises the issue of how local government can reconcile maintaining levels of service as the impacts of climate change and their uncertainties worsen over the coming decades (and beyond). Can they be adapted over time to retain levels of service or will they eventually require retreat and if so at what adaptation threshold? This paper explores managed retreat of two-waters infrastructure (wastewater and stormwater) as an adaptation option using a Dynamic Adaptive Pathway Planning (DAPP) approach. In the study, we use DAPP to frame the retreat of two-water networks, developing a combination of an area specific retreat strategy, pathway portfolios, retreat phases, land use change signaling and identify pathway conflicts and synergies. Repurposing retreated areas by utilizing Water Sensitive Urban Design (WSUD) options was found to extend retreat thresholds for adjacent areas. A systematic ’routine’ developed in this study provides a structured approach for managed retreat of two-water infrastructure with the aim to reduce future disruption from flooding, signal land use changes early and allow for gradual budget adjustments by the agencies to manage expenditure over time. This approach helps inform and improve the decision-making process for the agencies and the communities they serve, by providing a stepwise process that can be communicated spatially and visually, thereby making a retreat adaptation option more manageable.

The human casualties from simulated nuclear detonation scenarios in New Delhi, India are analyzed, with a focus on the distribution of casualties in urban environments and the theoretical application of a nuclear-specific triage system. Model estimates of nuclear war casualties employed ESRI's ArcGIS 9.3, blast and prompt radiation were calculated using the Defense Nuclear Agency's WE program, and fallout radiation was calculated using the Defense Threat Reduction Agency's (DTRA's) Hazard Prediction and Assessment Capability (HPAC) V404SP4, as well as custom GIS and database software applications. ESRI ArcGISTM programs were used to calculate affected populations from the Oak Ridge National Laboratory's LandScanTM 2007 Global Population Dataset for areas affected by thermal, blast and radiation data. Trauma, thermal burn, and radiation casualties were thus estimated on a geographic basis for New Delhi, India for single and multiple (six) 25 kiloton (kt) detonations and a single 1 megaton (1000kt) detonation. Major issues related to the emergency management of a nuclear incident are discussed with specific recommendations for improvement. The consequences for health management of thermal burn and radiation patients is the worst, as burn patients require enormous resources to treat, and there will be little to no familiarity with the treatment of radiation victims.

Geijera Schott is a plant genus of the Rutaceae Juss. (rue and citrus) family, comprising six species which are all native to Oceania. Of the plants belonging to this genus, the most significant species that has a customary use is Geijera parviflora, which was used by Indigenous Australians, primarily as a pain reliever. Herein, a comprehensive review of the literature published on the genus Geijera from 1930-2023 was conducted. This is the first review for this plant genus and it highlights the chemical constituents reported to date, together with the range of pharmacological properties described from the various species and different parts of the plant. These properties include anti-inflammatory, anti-microbial, anti-parasitic, insect repellent, analgesic, neuroactive, and anti-cancer activities. Finally, a reflection on some of the important areas for future focused studies of this plant genus is provided.

While it is generally accepted that food habits established during infancy will track into later childhood, longitudinal analysis of children’s food preferences is rare. This paper examines whether maternal-reported child food preferences at five years of age are the same as that reported at two years; and identifies any patterns of change from two- to five- years. Mothers in the Australian NOURISH trial reported child food preferences at two and five years of age. A four point scale was utilised - ‘like’, ‘neither like or dislike’, ‘dislike’, ‘never tried’. The proportion of children having the same preference at the two time points was calculated (95%CI) for 48 foods (cereals, 4; vegetables, 20; fruit, 14; meat/alternatives, 6; dairy, 4). For foods where ≤50% children had consistent preferences, the pattern of food preference change was determined. For 40/48 foods, more than half of the children were reported to have the same preference at two years of age, and three years later, at age five. Foods for which ≤50% children had the same preference at both ages were high-sugar breakfast cereals, zucchini, mushrooms, eggplant, spinach, lettuce, cabbage and celery. Findings reinforce the importance of promoting a consistent message regarding early and frequent exposure to a variety of healthy foods, particularly during the first 2 years of life, as the preferences established in these early years are likely to be maintained over time.

We show that loophole-free Bell-type no-go theorems cannot be derived in theories involving local hidden fields. At the time of measurement, a contextuality loophole appears because each particle’s electromagnetic field interacts with the field of its respective apparatus, preventing the expression of the probability density as a function independent of the orientation of the measuring devices. Then, we use the dynamical evolution of the probability distribution to show that the spin-correlation integral can neither be expressed in terms of initial Cauchy data restricted to the particles. A correlation loophole ensues, which prevents the usage of the non-contextual correlation integrals required to demonstrate the CHSH-Bell inequality. We obtain a new inequality not violated by quantum correlation functions of entangled spin pairs, and propose that Maxwell’s electrodynamic field is the missing hidden variable triggering the coupled nonlinear oscillations of the particles, which bring about the synchronicities observed in the Einstein-Podolsky-Rosen-Bohm (EPRB) experiment.

Motivated by Kim-Kim [19] introduced the new type of degenerate poly- Bernoulli polynomials by means of the degenerate polylogarithm function. In this paper, we define the degenerate poly-Frobenius-Euler polynomials, called the new type of degenerate poly-Frobenius-Euler polynomials, by means of the degenerate polylogarithm function. Then, we derive explicit expressions and some identities of those numbers and polynomials.

Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Frobenius-Genocchi polynomials. We derive the diverse formulas and identities covering some summation formulas, derivative formula and correlations with Bernoulli polynomials and numbers, Stirling numbers of the both kinds, degenerate Frobenius-Genocchi polynomials and degenerate Frobenius-Euler polynomials. Moreover, by using the unipoly function as following Kim-Kim's work in <cite>Kim1</cite>, we consider degenerate unipoly-Frobenius-Genocchi polynomials and investigate some formulas and relationships with Daehee numbers, degenerate Frobenius-Genocchi numbers and Stirling numbers of the first kind. Finally, we obtain an Gaussian integral representation of the Frobenius-Genocchi polynomials in terms of the 2-variable Hermite polynomials.

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

In this paper, we introduce a new class of Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Hermite-Fubini numbers and polynomials by using generating functions.

In the paper, the authors establish two identities, which can be regarded as nonlinear differential equations, for the generating function of Eulerian polynomials, find two identities for the Stirling numbers of the second kind, and present two identities for Eulerian polynomials and higher order Eulerian polynomials, pose two open problems about summability of two finite sums involving the Stirling numbers of the second kind. Some of these conclusions meaningfully and significantly simplify several known results.

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

A unified presentation of a class of Humbert’s polynomials in two variables which generalizes the well known class of Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinnsy, Horadam-Pethe, Djordjević , Gould, Milovanović and Djordjević, Pathan and Khan polynomials and many not so called ’named’ polynomials has inspired the present paper and the authors define here generalized Humbert-Hermite polynomials of two variables. Several expansions of Humbert- Hermite polynomials, Hermite-Gegenbaurer (or ultraspherical) polynomials and Hermite- Chebyshev polynomials are proved.

The main aim of this paper is to investigate multifarious properties and relations for the gamma distribution. The approach to reach this purpose will be introducing a special polynomial including gamma distribution. Several formulas covering addition formula, derivative property, integral representation and explicit formula are derived by means of the series manipulation method. Furthermore, two correlations including Bernoulli and Euler polynomials for gamma distribution polynomials are provided by utilizing of their generating functions.

The aim of this study was to quantify methane (CH4) emissions from dairy cows during milking by maximum amplitude of eructation peaks and compare estimates with other metrics for CH4 emissions. Spot measurements of CH4 and carbon dioxide (CO2) emissions were recorded for at least 7 days of continuous sampling using an infrared gas analyser in a robotic milking station whilst cows were milked. Concentrations of CH4 and CO2 were measured at 1 second intervals. A total of 105,701 CH4 spot measurements were obtained from 2,206 dairy cows on 18 farms. Methane emissions per individual cow were quantified by maximum amplitude of eructation peaks, average area under eructation peaks (integral of eructation), average concentration during milking and ratio of CH4 to CO2 concentration. There was a high correlation (r = 0.71) between CH4 emissions quantified by maximum amplitude and integral of eructation peaks. The correlation between maximum amplitude and average CH4 concentration was low, and there was no correlation between maximum amplitude and ratio of CH4 to CO2. As both approaches identify and extract eructation peaks to quantify enteric CH4 emissions, the substantial association between maximum amplitude and eructation integral was expected.

In this paper, we consider the zero distributions of q-shift monomi-als and difference polynomials of meromorphic functions with zero order, that extends the classical Hayman results on the zeros of differential poly-nomials to q-shift difference polynomials. We also investigate problem of q-shift difference polynomials that share a common value.

We introduce the lower chaos grade of a real-valued function F defined on the Markov triple (E,μ,Γ), where μ is a probability measure and Γ is the carré du champ operator. As an application of this concept, we obtain the better estimate of the four moments theorem for Markov diffusion generators worked by Bourguin et al (2019). For our purpose, we need to find the largest number except zero in the set of eigenvalues corresponding to its eigenfunction in the case where the square of a random variable F, coming from a Markov triple structure, can be expressed as a sum of eigenfunctions, We give some examples of eigenfunctions of the diffusion generators such as Ornstein-Uhlenbeck, Jacobi and Romanovski-Routh. In particular, two bounds, called the four moments theorem and fourth moment theorem respectively, will be provided for the normal approximation of the case where a random variable F comes from eigenfunctions of a Jacobi generator.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

In this paper, we introduce a new type of degenerate poly-Fubini polynomials and numbers, are called degenerate poly-Fubini polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we also consider the degenerate unipoly-Fubini polynomials attached to an arithmetic function, by using the degenerate polylogarithm function and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

In this paper, we construct the degenerate poly-Fubini polynomials, called the type 2 degenerate poly-Fubini polynomials, by using the modified degenerate polyexponential function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we introduce type 2 degenerate unipoly- Fubini polynomials attached to an arithmetic function, by using the modified degenerate polyexponential function and investigate some identities for those polynomials. Furthermore, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

In this paper, we introduce a new class of Laguerre-based Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Laguerre-based Hermite-Fubini numbers and polynomials by using generating functions.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

In Sub-Saharan Africa, despite poverty, chronic hunger and food insecurity, traditional eating has been related to positive health outcomes and sustainability. There is little health research on diet quality based on what African people consume. The defining characteristics of the traditional African cuisine are the richness in herbs and spices, fermented foods and beverages, and healthy and whole ingredients used. However, as countries in this region become more economically developed, there is a shift to “modern” occidental foods rich in saturated fats, sugar and sweeteners. As a result, there are increased incidences of previously unreported ailments due to unbalanced diet. The regular practice of infinite international aid to the region to curb food insecurity has been unsustainable, ineffective and with no end in sight. Local increase in production and productivity is imperative. Protein rich foods in dietary guidelines enhance only those of animal or plant sources while rich protein sources such of mushroom, has been absent in these charts. This article considers the valorisation of traditional African foods and the importance of establishing an African Food-Based Dietary Guidelines (AFBDGs), an unprecedented Food Pyramid, along with the added emphasis on the potential of African mushrooms, which may play a role in shielding Sub-Saharan Africans against the side-effects of a western stylish diet and promote health. It enhances the preventive role of mushrooms in viral diseases and other disorders.

When farmers first shift from conventional tillage (CT) to conservation agriculture (CA) practice the control of weeds may be more difficult due to the absence of tillage. However, in the longer term (3-5 years), CA changes to weed dynamics may alter the weed seedbank. The nature of weed seedbank changes over time in intensively cropped rice-based rotations, that are typical of the Eastern Gangetic Plain, are not well understood. Three long term CA experiments were sampled (at Rajbari after 3 years and Rajshahi after 5 years) for effects of decreased soil disturbance strip planting (SP) and bed planting (BP) at both sites and Zero tillage (ZT) at Rajbari, increased retention of standing residues of previous crops (20 vs 50 %). The weed seedbank in 0-15 cm soil was quantified by assessing emergence from trays a net-house experiment during January-December 2016. The year-round count of emerged weeds revealed the fewest number of weed species (especially broadleaf weeds) and lowest weed density in SP followed by CT, BP, and ZT with 50% crop residues. The SP, BP, and ZT produced a higher number of perennials weeds than annual weeds, which was the opposite of CT. The continuous practice of SP and increased crop residue retention for 3 or more years decreased the size of weed seedbank but increased the relative proliferation of perennial weeds compared to CT. Weed seedbank size in SP was even smaller than BP and ZT.

We propose a correspondence between partition functions of ideal gases consisting of both bosons and fermions and algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sides sequences ℓ1(Z0). Such an approach allows us to interpret some combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence on ℓ1(Z0) induced by the supersymmetric polynomials, and semiring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semiring structures on this set and discuss their possible physical interpretations.

In this paper we consider Changhee polynomials of type two, which are motivated from the recent work of Kim and Kim. We investigate some symmetry identities for the Changhee polynomials of type two which are derived from the properties of symmtery for the fermionic p-adic integral on Zp.

We investigate the value distribution of dierence polynomials of entire and meromorphic functions, which can be viewed as the Hayman's conjecture. And we also study the uniqueness of dierence polynomials sharing a common value.

In this paper, we introduce a new generalization of the Hermite polynomials via (p, q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also de…ne a (p, q)-analogue of the Bernstein polynomials and acquire their some formulas. We then provide some (p, q)-hyperbolic representations of the (p, q)-Bernstein polynomials. In addition, we obtain a correlation between (p, q)-Hermite polynomials and (p, q)-Bernstein polynomials.

On-farm research was conducted at Gouripur sub-district under Mymensingh district of Bangladesh during the boro (mid November-June) season in 2013-14 and 2014-15 to evaluate the performance of non-puddled rice cultivation with and without crop residue retention. The rice var. BRRI dhan28 was transplanted by two tillage practices viz., puddled conventional tillage (CT) and non-puddled strip tillage (ST) and at two levels of mustard residues, i.e., no residue (R₀) and 50% residue (R₅₀). The experiment was designed in a randomized complete block design with four replications. There were no significant yield differences between tillage practices and residue levels in 2013-14. But in the following year, ST yielded 9% more grain compared to CT leading to 22% higher BCR. Retention of 50% residue increased yield by 3% compared to no-residue, which contributed to 10% higher benefit-cost ratio (BCR). The ST combined with 50% residue retention yielded the highest grain yield (5.81 t ha^-1) which contributed to produce the highest BCR (1.06).

Background: Down Syndrome is the most well-studied aneuploidy condition in humans. It is associated with multiple disease phenotypes including cardiovascular, neurological, haemato-logical, and immunological disease processes. In this review paper we aim to discuss the research into gene expression studies performed at the fetal stage of development. Methods: A descriptive review was performed including all papers published on the PubMed database between Septem-ber 1960- September 2022. Results: In the amniotic fluid, genes such as COL6A1 and DSCR1 are affected, causing the phenotypical craniofacial changes. Other genes affected in amniotic fluid in-cluding: GSTT1, CLIC6, ITGB2, C21orf67, C21orf86 and RUNX1. In the placenta, MEST, SNF1LK and LOX were dysregulated, affecting nervous system development. In the brain DYRK1A, DNMT3L, DNMT3B, TBX1, olig2 and AQP4 were found to be dysregulated, affecting the nervous system and intellectual disability. In the cardiac tissues GART, EST2 and ERG found to be dysregulated causing secondary heart field abnormalities. XIST, RUNX1, SON, ERG and STAT1 dysregulated causing myeloproliferative disorders. Conclusions: Differential expression of genes provides clues to the genetic consequences of DS. A better understanding of these processes could eventually to lead to the development of genetic and pharmacological therapies.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Z_p of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.

Motivation by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim [9], in the present paper, we consider a new class of new generating function for the Fubini polynomials, called the type 2 poly-Fubini polynomials by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Fubini polynomials equal a linear combination of the classical of the Fubini polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Fubini polynomials and Bernoulli polynomials of order r. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim [9]. We introduce the type 2 unipoly-Fubini polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Fubini polynomials and the classical Fubini polynomials.

In this paper, we consider a new class of polynomials which is called the multi-poly-Euler polynomials. Then, we investigate their some properties and relations. We provide that the type 2 degenerate multi-poly-Euler polynomials equals a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers.

Inspired by the definition of degenerate multi-poly-Genocchi polynomials given by using the degenerate multi-polyexponential functions. In this paper, we consider a class of new generating function for the degenerate multi-poly-Bernoulli polynomials, called the type 2 degenerate multi-poly-Bernoulli polynomials by means of the degenerate multiple polyexponential functions. Then, we investigate their some properties and relations. We show that the type 2 degenerate multi-poly-Bernoulli polynomials equals a linear combination of the weighted degenerate Bernoulli polynomials and Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Bernoulli numbers and degenerate Whitney numbers.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on ℤ_{p} of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

In this paper, we introduce a new class of $(p,q)$-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for $(p,q)$-Fubini polynomials associated with $(p,q)$-Bernoulli polynomials, $(p,q)$-Euler polynomials and $(p,q)$-Genocchi polynomials and $(p,q)$-Stirling numbers of the second kind.