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In this article, we determine various analytical solutions for the (4 + 1) -dimensional Fokas equation, a significant model in mathematical physics with numerous applications in nonlinear dynamics. Utilizing multiple integration techniques such as the improved F-expansion technique and the Jacobi elliptic function method, we retrieve an array of solution types, including traveling waves, periodic solutions, bell-shaped waves, rational functions, and both kink and anti-kink structures. We further explore the complex nature of these solutions through their graphical representations. By applying Maple, we visualize our results in three-dimensional (3D), and two-dimensional (2D) formats to illustrate the dynamic behavior of these solutions across various parameters and initial conditions. Our findings provide deeper insights into the properties of the Fokas equation and offer a valuable reference for further studies in nonlinear wave phenomena. [ABSTRACT FROM AUTHOR]

The present study is focused on evaluating acaricidal activity and chemical compositions of Erigeron acer root, which was identified as a promising candidate among fifteen Mongolian plant extracts tested for acaricidal activity. The acaricidal effect was evaluated against Haemaphysalis longicornis, assessed for toxicity to normal human skin fibroblast, and analyzed for its chemical constituents. The acetone extract of E. acer root showed significant activity against H. longicornis, with a lethal concentration (LC50) of 5.31 mg/mL and low toxicity, evidenced by a cytotoxic concentration (CC50) of 267.00 µg/mL. Using liquid chromatography-tandem mass spectrometry and molecular networking, thirteen natural compounds were identified, including pyrrolidines, alkaloids, fatty acids, and flavonoids, highlighting the efficacy of E. acer root extract as an effective acaricide against H. longicornis and offering insights for developing new tick control solutions. [ABSTRACT FROM AUTHOR]

Tree growth is a key mechanism driving carbon sequestration in forest ecosystems. Environmental conditions are important regulators of tree growth that can vary considerably between nearby urban and rural forests. For example, trees growing in cities often experience hotter and drier conditions than their rural counterparts while also being exposed to higher levels of light, pollution, and nutrient inputs. However, the extent to which these intrinsic differences in the growing conditions of trees in urban versus rural forests influence tree growth response to climate is not well known. In this study, we tested for differences in the climate sensitivity of tree growth between urban and rural forests along a latitudinal transect in the eastern United States that included Boston, Massachusetts, New York City, New York, and Baltimore, Maryland. Using dendrochronology analyses of tree cores from 55 white oak trees (Quercus alba), 55 red maple trees (Acer rubrum), and 41 red oak trees (Quercus rubra) we investigated the impacts of heat stress and water stress on the radial growth of individual trees. Across our three‐city study, we found that tree growth was more closely correlated with climate stress in the cooler climate cities of Boston and New York than in Baltimore. Furthermore, heat stress was a significant hindrance to tree growth in higher latitudes while the impacts of water stress appeared to be more evenly distributed across latitudes. We also found that the growth of oak trees, but not red maple trees, in the urban sites of Boston and New York City was more adversely impacted by heat stress than their rural counterparts, but we did not see these urban–rural differences in Maryland. Trees provide a wide range of important ecosystem services and increasing tree canopy cover was typically an important component of urban sustainability strategies. In light of our findings that urbanization can influence how tree growth responds to a warming climate, we suggest that municipalities consider these interactions when developing their tree‐planting palettes and when estimating the capacity of urban forests to contribute to broader sustainability goals in the future. [ABSTRACT FROM AUTHOR]

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The study of the elements of mathematical logic and its sections, especially in the process of teaching in high school in general and specialized courses of mathematics or higher educational institutions, is a rather tricky task. The paper demonstrates how one can design and develop a package of interactive applications to help learn, understand, and apply the essential elements of mathematical logic. The research aims to develop and describe an interactive application for studying the order of constructing truth tables and studying and demonstrating the production of principal normal disjunctive and conjunctive forms. The development is based on the methods of the Maple computer algebra system of the Maplet library. In addition, other methods are used to solve the research issues - theoretical and accurate analytical solutions to mathematical logic issues. All constructed material (Maplet) will serve as a good simulator for students, allowing one to perform an infinite number of attempts to analyze, synthesize, and build truth tables. [ABSTRACT FROM AUTHOR]

In this research work, it has examined the mathematical model such as SIR, for infectious diseases as a novel coronavirus (COVID-19). This model has played a vital role in various fields of epidemiology and environmental sciences. In addition, these types’ models are very beneficial to know about the infectious diseases’ dynamical behavior. In this work, the nonlinear COVID-19 model’s dynamical behavior is based on a semianalytical technique: Variational Iteration Method (VIM). Further, to describe the COVID-19 model, we create a novel signal flow graph. Our mathematical analyses assist us that the spread of the virus may be controlled by maintaining social distance between infected individuals and healthy individuals. Also, the analytical solution of the aforesaid mathematical model will be calculated with the help of computational software such as MAPLE code. In the end, the results will be compared with other numerical techniques to show the efficiency of the aforementioned techniques. [ABSTRACT FROM AUTHOR]

Stochastic reasoning must be part of the comprehension of chemical and physical processes that occur in Nature. Stochastic phenomena can be found in several natural observations and in numerous Chemical Engineering related issues, such as optimization, process control, molecular diffusion, and chemical reaction kinetics. In the present work, an Activity Based Learning (ABL) approach is used to contribute to the teaching and learning process of stochastic differential equations (SDE). The focus is on the solution of the SDE and its parametric evaluation starting from the classic stochastic equations. The choice of the parameters is a key learning step that is useful to explore some aspects of the problem phenomenology and to promote critical reasoning in the students. Two different tools with specific modules to handle and solve SDE were used: the proprietary Maple tool with Finance and Stochastic Processes models and an open-source tool developed in Python, the sdeint of PyPi. • Active tasks are proposed viewing the learning of stochastic differential equations (SDE) in Chemical Engineering. • The focus is on the solution of the SDE and its parametric evaluation. • The modules Finance and Stochastic Processes of MAPLE are used. • Python and sdeint approach are used as well. • The student may understand SDE from a hands-on process. [ABSTRACT FROM AUTHOR]

In this research, Genocchi wavelets method, a quite new type of wavelet-like basis, is adopted to obtain a numerical solution for the classical and time-fractional Rosenau-Hyman or K (n , n) equation arising in the formation of patterns in liquid drops. The considered partial differential equation can be transformed into a system of non-linear algebraic equations by utilizing the wavelets method including an integral operational matrix and then discretizing the equation at the collocation points. The system can be simply solved by several traditional methods. Finally, the algorithm is implemented for some numerical examples and the numerical solutions are compared with the exact solutions using MAPLE. The obtained results are demonstrated using figures and tables. When the results are compared, it is evinced that the algorithm is quite effective and advantageous due to its easily computable algorithm, high accuracy, and less process time. [ABSTRACT FROM AUTHOR]

Businesses can gain strength and thus purposefully optimize their commercial models by means of implementing open innovations. The innovation process is increasingly conditioned by the innovative activities of customers. It is necessary to perform quick, low-cost, and rational research so that outputs can be updated and implemented into business models in-time. Digital transformation supports these processes because it represents a good opportunity for free spatial-temporal communication, and for the timely interaction of the participating parties. This contribution stems from research (under the supervision of the paper's co-author, von Böhlen, 2021) performed in the German automotive industry, and follows up on the work of Simberova and von Böhlen (2021). The aim is to perform further and more detailed analyses and to interpret facts that ensue from selected research outputs. These analyses are oriented solely towards the issue of open innovations as seen from the customer's perspective: innovations used for scaling business models in the automotive industry. Focus is especially placed on factors and relationships which affect customers' willingness to enter the open innovations process. The customer's social status has been taken into account. The rate and willingness of customers to engage in innovation activities has been measured - in connection with a whole range of factors, especially financial, those based on benefits, and others. Another form of analysis was a statistical evaluation that identified the degree of interest in some selected types of benefits. The independence of selected agents that stem from the survey evaluation was also considered, and quantitative methods, mainly statistical calculations, and transparent statistical visualizations were employed for this purpose. The methods of descriptive statistics and categorical analysis were used for processing data sets in the environment of the advanced Maple System. These findings confirm that the customer is becoming a non-stationary and important source of information and possibly also a source of inferences regarding open innovations. Society is thus increasing its potential to work not only for the customer, but also with them. It is necessary to be ready to react to current pitfalls and to communicate with the customer continuously. Pertaining to implementing open innovations, these analyses have given interesting concrete output and findings regarding decision-making in the process of amplifying the business model in the automotive industry, as seen from the customer's viewpoint, and in the era of digitization. Further, they have opened a whole range of challenges related to further analyses of the matter at hand. [ABSTRACT FROM AUTHOR]

The mathematical study of epidemics and their management has been performed for many years, however, in the last few years, new models have been published. Public health is considered very important and has to be monitored, as it is permanently under risk due to the appearance of even more types of microorganisms. Compartmental models, such as exponential models, SI, SIS, SIR, SEIRS, SEIAR, MESIR models, other generalized SIR models were and still are remarkable for studying the spread of an epidemic and for their simulations in software such as MATLAB, Maple, GLEAMviz, etc. The paper has two main objectives: a. to present new simulations in Maple and GLEAMviz for the spread of COVID-19; b. to suggest a generalization of the SIR model for analyzing the spread of COVID-19 and a simulation of it in GLEAMviz. The conclusions are that, generally, mathematical models show a value of a reproduction threshold, which can be used to forecast whether the pandemic is the increasing or decreasing phase, and that mathematical models and simulations in various programs facilitate the improvement of methods of analysis of an epidemic situation and the management of the public health system. [ABSTRACT FROM AUTHOR]

We successfully prepared activated carbons (AC) derived from waste maple leaves and applied them to electrode materials for organic electric double-layer capacitors (EDLC). Maple leaves were efficiently converted into ACs based on their eco-friendliness, cost effectiveness, oxygen-containing, and inorganic components that can promote forming pores. Accordingly, waste maple leaves were carbonized under flowing nitrogen, and subsequently activated using CO2 or KOH to be converted into ACs with large specific surface areas. Particularly, a maple carbon sample chemically activated at 800 °C with KOH (MCK800) showed not only a large specific surface area but also well-developed pore structure, and the properties of MCK800 were superior to those of a commercially available activated carbon (YP50f). These remarkable properties of MCK800 led to considerable capacitance properties and high electrical conductivity in an organic EDLC system. Finally, we concluded that waste maple leaves are potential candidates for low-cost starting materials of organic EDLC electrodes. [ABSTRACT FROM AUTHOR]

Copyright of Ecoscience (Ecoscience) is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Urban trees can reduce stormwater runoff and mitigate flood risk by increasing infiltration, and storing water in the soil, while reducing nutrient loading, and improving water quality in developed areas. Tree water use can constitute a major component of evapotranspiration, but knowledge gaps about how the local environment affects transpiration limits our ability to predict how management will affect hydrology. In this study, we investigated the influence of management context on the transpiration of deciduous tree species and the relationship between environmental factors (soil moisture and vapor pressure deficit) and tree transpiration. We monitored sap flux rates of three common urban tree species, red maple, tulip poplar, and sweetgum (n=41 trees), during the 2018 and 2019 growing seasons in urban forest patches in Baltimore, MD, in addition to a cluster of trees over turfgrass and single trees over turfgrass in Montgomery County, MD. Management context influenced sap flux and, on a per-tree basis, single red maple trees had greater transpiration than red maple trees in a closed canopy setting in both years. The mean daily sum of sap flux density (Js) was 227, 163, and 87.5 g cm−2d−1 at the single, cluster, and closed canopy sites, respectively, for red maple trees, with some interannual variability primarily driven by weather conditions. Although Js was fairly similar across species in closed canopy conditions throughout the two growing seasons, species differences in sap flux density were observed at the diel (24-h) time scale with tulip poplar being the most sensitive to drought. We also developed whole-tree water use estimates based on DBH, species, and management context. Whole-tree water use varied directly with diameter. Plot-level water use through transpiration was 9.1, 71.2, and 52.4% of precipitation during April-October 2019 in the single, cluster, and closed canopy sites, respectively. These results provide an initial framework for estimating how urban forest management affects the hydrological balance, with useful implications for stormwater managers and modelers. [ABSTRACT FROM AUTHOR]

Acer mazandaranicum is an endemic, endangered, recently described large tree species distributed in the Hyrcanian forest. Only a few scattered populations with low density are known in the Alborz Mountains of Iran. This research aims to approximate the potential geographical distribution range of A. mazandaranicum in the past, present, and future to provide a basis for prioritizing conservation-related activities. For the contemporary climate model, two past scenarios and three future climate scenarios were tested. The most crucial variables, as determined by the model, were the seasonality of precipitation and the amount of precipitation during the driest quarter, which together constituted 90.9% of the model for current conditions and presented A. mazandaranicum climatic requirements for appropriate habitats. According to our findings, the potential habitat of the species will be drastically diminished in suitability in the future. The model projected an area of 7410.8 km2 as moderate suitability habitat (0.50–0.75) and 13,896.41 km2 as low suitability (0.25–0.50). The average altitude in the potential range is 1026 m a.s.l. During the LGM, the potential range of A. mazandaranicum was 209.27% of the current area and spread mainly at lower altitudes (1078.8 m a.s.l.). The findings indicate a fascinating possibility that the species may possess the capability to shift their altitudinal distribution and potentially migrate to higher elevations in response to increasing temperatures and decreasing rainfall. According to morphological spatial analysis (MSPA), the central and western regions of the Hyrcanian forests contain a core area with high connectivity. In order to mitigate the threats facing this endangered species and reduce the risk of extinction, ex situ conservation measures as well as in situ protection activities within their habitats are necessary for ensuring its long-term survival. • Precipitation seasonality and precipitation of the driest quarter are the most important factors of the presence of A. mazandaranicum. • During LGM, the potential range area of A. mazandaranicum was around 209% of the current, and around 14,962 km2 was estimated as moderate and high-suitability habitat during the LGM. • Potential habitat suitability of the species will shrink significantly in the future, and this is more worrying for A. mazandaranicum in comparison with the other members of the genus Acer in the Hyrcanian forest. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the free convection boundary-layer flow with heat generation and variable fluid properties past a vertical plate. We incorporated the heat generation and variable viscosity are the exponential decay form and thermal conductivity is the linear form in the governing equation. Using similarity transformations, the governing coupled non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations and then solved using Maple symbolic software to execute the computations via dsolve. The effects of the temperature-dependent viscosity, the wall velocity power index, the thermal conductivity, the wall temperature parameter, and the Prandtl number on the flow and temperature fields are presented. The skin friction and the wall temperature gradient are also presented for different values of the physical parameters. [ABSTRACT FROM AUTHOR]

In Brazil, we are interested in the study of second-order recurrent numerical sequences. Such mathematical content has an enormous potential to provide a differentiated mathematical culture for the math teachers in initial training. However, it becomes important that the teacher in Brazil knows properties beyond the traditional and classic numerical sequences, such as the Fibonacci sequence, Lucas sequence, Pell sequence, Jacobsthal sequence, Narayana sequence, etc. Thus, in the present work, we present a proposal of CAS Maple as technological resources in the study and discovery of new theorems derived from the Mersenne sequence. Throughout the work, we show that the software allows the discovery of theorems from matrix properties derived from the Mersenne sequences and the sequence of Gaussian numbers of Mersenne. The research presented in the paper can stimulate the formation of Mathematics teachers in Brazil. [ABSTRACT FROM AUTHOR]

• Group-selection openings modestly increase tree diversity in uneven-aged hardwoods. • Large openings (22 m radius) have highest regeneration richness and diversity. • Shade-tolerant Acer saccharum dominant in regeneration layers 15 years post-harvest. Group selection has been proposed as a complementary system to conventional, uneven-aged management in temperate hardwoods (i.e. single-tree selection) to counteract declines in overstory diversity and growing importance of shade-tolerant species caused largely by past management activities. Mixed results from experimental group selection harvests in eastern North America and growing interest in retention forestry have led some scientists and managers to apply ideas from retention forestry into group selection systems. The Yellow Birch Legacy-Tree Project is a group selection experiment established in 2003, which incorporates single, dominant/co-dominant yellow birch (Betula alleghaniensis Britt.) legacy-trees into the centers of harvested canopy gaps in a northern hardwoods forest in the Upper Peninsula of Michigan. Group selection openings (n = 49) in three size classes based upon radii—small (11 m, n = 16), medium (16.5 m, n = 17), and large (22 m, n = 16)—were surveyed alongside single-tree selection reference sites (n = 20) 15 years post-harvest. Our goals were to (1) examine long-term trends in seedling and sapling abundance and diversity, (2) evaluate the initial and contemporary effects of gap size on regeneration, and (3) assess the overall efficacy of group-selection with legacy-tree retention in regenerating mid-tolerant and intolerant species, especially yellow birch. At 15 years post-harvest, we found that shade-tolerant sugar maple (Acer saccharum Marsh.) dominated regeneration layers across all treatments, but we observed modest increases in seedling and sapling diversity within openings that may alter long-term canopy composition over several cutting cycles. We found that gains in diversity and evenness in canopy gaps persisted through time and that large gaps (22 m radius) had the most species-rich and diverse regeneration compared to reference sites. Canopy gaps contained significantly higher densities of shade-intolerant and mid-tolerant seedlings and saplings compared to reference sites, namely red maple (Acer rubrum L.), black cherry (Prunus serotina Ehrh.), and yellow birch; however, most diversity occurred in shorter height classes. Nevertheless, legacy retention within group selection systems holds promise for maintaining ecological memory and structural complexity through time, but further treatments such as scarification may be necessary to shift compositional trajectories in favor of shade-intolerant and mid-tolerant species. [ABSTRACT FROM AUTHOR]

We used data on a forest-based ecosystem service, sugar maple (Acer saccharum) sap, spanning sugar maple's latitudinal range to predict the role of climate variation on two aspects of sap productivity: sugar content and sap flow. The sugar in maple sap is derived from carbohydrate stores influenced by growing season conditions in the prior year, while sap flow is tied to freeze/thaw cycles during early spring. Our findings suggest optimal regions for sap production will move northward, with lower average production across nearly the entire range except for the far north, and provide spatially-explicit projections for forest managers and syrup producers making decisions on the location and viability of management for maple syrup production. Climate change is affecting the benefits society derives from forests. One such forest ecosystem service is maple syrup, which is primarily derived from Acer saccharum (sugar maple), currently an abundant and widespread tree species in eastern North America. Two climate sensitive components of sap affect syrup production: sugar content and sap flow. The sugar in maple sap derives from carbohydrate stores influenced by prior year growing season conditions. Sap flow is tied to freeze/thaw cycles during early spring. Predicting climate effects on syrup production thus requires integrating observations across scales and biological processes. We observed sap at 6 sugar maple stands spanning sugar maple's latitudinal range over 2–6 years to predict the role of climate variation on sugar content and sap flow. We found that the timing of sap collection advanced by 4.3 days for every 1 °C increase in March mean temperature, sap volume peaked at a January-May mean temperature of 1 °C, and sap sugar content declined by 0.1 °Brix for every 1 °C increase in previous May-October mean temperature. Using these empirical relationships, we projected that the sap collection season midpoint will be 1 month earlier and sap sugar content will decline by 0.7 °Brix across sugar maple's range by the year 2100 in an RCP 8.5 climate change scenario. The region of maximum sap flow is expected to shift northward by 400 km, from near the 43rd parallel to the 48th parallel by 2100. Our findings suggest climate change will have profound effects on syrup yield across most of sugar maple's range; drastic shifts in the timing of the tapping season accompanied by flat to moderate increases in syrup yield per tap in Canada contrast with declines in syrup yield and higher frequencies of poor syrup production years across most of the U.S. range. [ABSTRACT FROM AUTHOR]

In this article, we develop the traditional differential equation for Foucault's pendulum from physical situation and solve it from standard form. The sublimation of boundary condition eliminates the constants and choice of the local parameters (latitude, pendulum specifications) offers an equation that can be used for a plot followed by animation using MAPLE. The fundamental conceptual components involved in preparing differential equation viz; (i) rotating coordinate system, (ii) rotation of the plane of oscillation and its dependence on the latitude, (iii) effective gravity with latitude, etc., are discussed in detail. The accurate calculations offer quantities up to the sixth decimal point which are used for plotting and animation. This study offers a hands-on experience. Present article offers a know-how to devise a Foucault's pendulum just by plugging in the latitude of reader's choice. Students can develop a miniature working model/project of the pendulum. [ABSTRACT FROM AUTHOR]