Seasonal influence of freshwater discharge on spatio-temporal variations in primary productivity, sea surface temperature, and euphotic zone depth in the northern Bay of Bengal

Ocean productivity is the foundation of marine food web,which continuously removes atmospheric carbon dioxide and supports life at sea and on land.Spatio-temporal variability of net primary productivity(NPP),sea surface temperature(SST),sea surface salinity(SSS),mixed layer depth(MLD),and euphotic zone depth(EZD) in the northern B ay of Bengal(BoB) during three monsoon seasons were examined in this study based on remote sensing data for the period 2005 to 2020.To compare the NPP distribution between the coastal zones and open BoB,the study area was divided into five zones(Z1-Z5).Results suggest that most productive zones Z2 and Zl are located at the head bay area and are directly influenced by freshwater discharge together with riverine sediment and nutrient loads.Across Z1-Z5,the NPP ranges from 5 315.38 mg/(m^(2)·d) to 346.7 mg/(m^(2)·d)(carbon,since then the same).The highest monthly average NPP of 5 315.38 mg/(m^(2)·d) in February and 5 039.36 mg/(m^(2)·d) in June were observed from Z2,while the lowest monthly average of 346.72 mg/(m^(2)·d) was observed in March from Z4,which is an oceanic zone.EZD values vary from 6-154 m for the study area,and it has an inverse correlation with NPP concentration.EZD is deeper during the summer season and shallower during the wintertime,with a corresponding increase in productivity.Throughout the year,monthly SST shows slight fluctuation for the entire study area,and statistical analysis shows a significant correlation among NPP,and EZD,overall positive between NPP and MLD,whereas no significant correlation among SSS,and SST for the northern BoB.Long-term trends in SST and productivity were significantly po sitive in head bay zones but negatively productive in the open ocean.The findings in this study on the distribution of NPP,SST,SSS,MLD,and EZD and their seasonal variability in five different zones of BoB can be used to further improve the management of marine resources and overall environmental condition in response to climate changes in BoB as they are of utmost relevance to the fisheries for the three bordering countries.

Small Modular Solutions to Fermat’s Last Theorem

The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.

Feasibility of Plug Production Utilizing Digestate from Home-Waste to Energy Systems (H-WEF)

The integration of sustainable technologies in waste management systems has become imperative in addressing the escalating challenges of agricultural productivity and sustainability. Plugs are essential when starting crop production in controlled environment agriculture (CEA) setups and greenhouses. Horticultural crops such as vegetables, fruiting, and ornamental plants that utilize plugs have demonstrated higher success rates, healthier plants, and higher total yields. The APS Laboratory for Sustainable Agriculture explored the innovative utilization of digestate from the Home Water-Energy-Food Systems (H-WEF). The H-WEF system converts household food waste into biogas, electricity, and nutrient-rich digestate. The digestate from the H-WEF system was used to produce agricultural plugs, presenting a novel approach to circular resource utilization. We carried out the growth of Rex Butterhead Lettuce Latuca sativa plugs with 1) control system (synthetic fertilizer) and seven different treatments, 2) 5% Digestate—95% RO Water (5D–95RO);3) 10% Digestate—90% RO Water (10D–90RO);4) 15% Digestate—85% RO Water (15D–85RO);5) 20% Digestate—80% RO Water (20D–80RO);6) 25% Digestate—75% RO Water (25D–75RO);7) 30% Digestate—70% RO Water (30D–70RO);8) 35% Digestate—65% RO Water (35D–65RO). The plugs were cultivated for 15 days in a controlled environment until two leaves had developed after the cotyledon. After 15 days, we collected data on wet weight (g), plug head area (cm2), total leaf area (cm2), total chlorophyll content (mg/cm2), and dry weight (g). In addition, we collected data on the Leaf Area Index (LAI, cm2/cm2) and Specific Leaf Area (SLA, cm2/g). The synthetic fertigation yielded a higher wet weight than the following treatments: 5D–95RO, 10D–90RO, and 35D–65RO. While the 30D–70RO treatment produced a larger plug head than all other treatments. The digestate-based fertilizers were comparable to the synthetic fertilizer at dilutions of 25D–75RO and 30D–70RO. This study underscores the viability of using digestate for plug production, providing crucial insights for growers navigating the challenges of sustainable agricultural practices.

Controlled Environment Agriculture and Its Ability to Mitigate Food Insecurity

The research objective of this review is to discuss the rationale that led to the development of Controlled Environment Agriculture (CEA) and investigate this agricultural approach as a potential solution to mitigate the increased pressures on food security. It describes the need for urban cultivation systems using controlled environments and how they can be harnessed to address pressures facing food security. The factors that have contributed to the growth of CEAs, education, environmental justice, and the advantages and disadvantages of growing crops in CEAs in urban areas will be discussed. The article reviews global urban cultivation systems using controlled environments, by identifying the technologies needed to establish them. The practice of CEA is being increasingly adopted worldwide and we describe urban agriculture and compare it with traditional growing systems. Indoor farming systems that integrate into existing urban infrastructure such as vertical farming and plant factories using CEAs are discussed. Indoor farming gives urban areas enhanced access to food sources, but the cost is high, however decreasing due to recent technological advances. The current review extends the literature by incorporating recent research on the topic of agriculture in urban areas and food security. This review seeks to provide additional information regarding the viability of CEA in urban areas.

Generalized Series of Bernoulli Type

The problem of evaluating an infinite series whose successive terms are reciprocal squares of the natural numbers was posed without a solution being offered in the middle of the seventeenth century. In the modern era, it is part of the theory of the Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve it by considering other more tractable series which were superficially similar and which he hoped could be algebraically manipulated to yield a solution to the difficult series. This approach was eventually unsuccessful, however, Bernoulli did produce an early monograph on summation of series. It remained for Bernoulli’s student and countryman Leonhard Euler to ultimately determine the sum to be . We characterize a class of series based on generalizing Bernoulli’s original work by adding two additional parameters to the summations. We also develop a recursion formula that allows summation of any member of the class.

The Comparative Performance of Nutrient-Film Technique and Deep-Water Culture Method of Hydroponics for GREENBOX Technology

With the rising pressures on food security, GREENBOX technology was developed as an avenue for fresh leafy vegetable crop production in urban settings. GREENBOX units were designed to be thermally insulated and climate controlled, with an artificial lighting source that utilized soilless cultivation techniques. Previous studies conducted on GREENBOX technology used the Nutrient Film Technique (NFT);however, various hydroponic methods exist, such as the Deep-Water Culture (DWC) method being the most used. The APS Laboratory for Sustainable Food at Florida Gulf Coast University (FGCU) compared the crop growth performance between DWC and NFT systems using GREENBOX technology. The following study monitored environmental conditions and compared productivity and biomass data of Rex Butterhead Lettuce crops between DWC and NFT systems. We assembled two GREENBOX units using commercially available materials and the standard nutrient solution for fertigation. The crops grown in DWC and NFT were in a 4 × 6 configuration. The DWC and NFT systems were used to grow Lettuce Lactuca sativa “Rex Butterhead” over 30 days to full bloom from prepared plugs grown for 14 days. We collected environmental data including Photosynthetic Photon Flux Density (PPFD, μmol/m2∙s), Daily Light Integral (DLI, mol/ m2∙d), temperature (˚C), relative humidity (%), and Vapor Pressure Deficit (VPD, kPa). We collected lettuce crop growth data, which included wet weight (g), dry weight (g), leaf area (cm2), and chlorophyll concentration (μmol/m2). We derived data, including the Specific Leaf Area (SLA, cm2/g) and biomass productivity (kg/m2), from previously collected data. We used descriptive statistics to present the collected data. A paired t-test was performed to understand the differences in biomass and productivity parameters between the DWC and NFT-grown lettuce crops. Both the DWC and NFT-grown crops could grow lettuce crops to harvest weight at full bloom. Observed data demonstrated that the biomass parameters and productivity did not differ significantly between the two hydroponics techniques. Therefore, we believe both hydroponic methods may be similar in growth performance and may be used in future iterations of GREENBOX design and prove suitable for fresh vegetable crop production in urban settings.

The Comparative Performance of Plug Preparation Using Different Fertilizer Sources and Concentrations

Plugs are crucial for initiating crop production in greenhouses, soil, and controlled environment agriculture (CEA). Vegetable, fruiting, ornamental, and other horticultural crops that utilize plugs for production have demonstrated superior transplant establishment rate, plant health, and total yield. The APS Laboratory for Sustainable Food at Florida Gulf Coast University investigated the quality of plugs grown based on different concentrations and fertigation sources using synthetic and organic sources. We carried out the growth of “Rex Butterhead” Lettuce (Latuca sativa) plugs with five different fertigation treatments, 1) full-strength synthetic starter fertilizer solution;2) half-strength synthetic starter fertilizer solution;3) full-strength organic starter fertilizer solution;4) half-strength organic starter fertilizer solution, and 5) no fertilizer for control. Fertilizer treatments were formulated following manufacturer recommendations. The seeds were sown in Oasis® Horticubes and saturated every day with the different fertilizer treatments. The plugs were cultivated for 15 days in a controlled environment until two leaves after the cotyledons had developed. After 15 days, we collected data which included wet weight (g), dry weight (g), leaf area (cm2), and chlorophyll concentration (mg/cm2). In addition, we derived data including the Leaf Area Index (LAI, cm2/cm2) and Specific Leaf Area (SLA, cm2/g). Descriptive statistics were used to describe the biomass data. A Tukey’s HSD test was carried out to understand the differences between the fertilizer sources. We determined there was a statistically significant difference (P = 7.34E−29) in the measured plug growth parameters due to the various fertigation sources. We found that all fertilizer treatments produced viable plugs except for the control treatment. Of all the treatments, we concluded the half-strength organic treatment produced the more vigorous plugs with the greatest wet weight (g) and largest total leaf area (cm2) which was statistically significantly different. Results from this study may inform growers about appropriate fertilizer options for plug production.

The Comparative Performance of Soil-Based Systems with Hydroponics

Conventional soil-based agriculture is resource-intensive, utilizing large amounts of land and water, thereby placing a strain on Earth’s natural resources. Soil-based agricultural techniques create environmental issues such as soil degradation, deforestation, and groundwater pollution from the mass implementation of fertilizers and pesticides. Agricultural crop production using hydroponics has shown promise to be less resource intensive and provide a faster turnaround in crop production. Soilless cultivation using hydroponics promises to relieve some pressure on Earth’s ecosystems and resources by utilizing lesser land and water footprint. The APS Laboratory for Sustainable Food at Florida Gulf Coast University (FGCU) compared the growth of Lettuce Lactuca sativa “Rex Butterhead” crop grown using soil and soilless methods to analyze the growth performance in each setting. Crops grown in the soil-based medium were raised in the FGCU Food Forest, used a mix of soil and potting mix, watered regularly, and followed standard Integrated Pest Management (IPM) practices. Crops grown hydroponically were grown in a thermally insulated grow tent with an artificial lighting source, ventilation, environmental controls, and the Deep-Water Culture (DWC) method. Lettuce plugs were grown for 15 days in controlled environments until two leaves after the cotyledons had developed and were ready for transplant. Plugs were transplanted into a 4 × 6 matrix at the FGCU Food Forest and the DWC growth system. Crops were grown to full bloom and ready for harvest in the soil (60 days) and soilless (30 days) based setups. We collected crop growth data, including wet weight (g), dry weight (g), leaf area (cm2), and chlorophyll concentration (μmol/m2). From the collected data, we derived the Specific Leaf Area (SLA, cm2/g) and biomass productivity (kg/m2). Descriptive statistics were used to describe the collected and derived data. We investigated the slopes of regression lines for each growth curve which derived the differences in biomass and productivity parameters between lettuce grown using soil and hydroponics. Both growing methods can grow lettuce crops to full bloom and to adequate harvest weight. The biomass parameters and productivity differ significantly between the growing methods. The lettuce crops grown using hydroponics increase in wet weight statistically and significantly faster than those grown in soil (p < 0.0001). Therefore, we determined that a hydroponic method of crop production may provide better crop output and biomass indicators measured than soil-based growth.

The Assessment of Growth Performance of Brassica rapa var. chinensis ‘Li Ren Choi’, Spinacia oleracea ‘Auroch’, Eruca sativa ‘Astro’, and Brassica rapa var. japonica Using GREENBOX Technology

Obtaining nutritious food is becoming increasingly difficult due to the growing urban population and the degradation of soil, water, and air from mechanized and industrialized agricultural techniques. More than half the global population resides in urban areas, with not enough surrounding agricultural land to meet food requirements. Food traveling long distances, an average of 1020 miles, has resulted in increased food miles for the average food item in the United States of America, representing wasted resources. The novel GREENBOX technology was invented in response to increasing pressures on food security. Previous studies conducted on GREENBOX technology assessed the technical feasibility of utilizing Lettuce Lactuca sativa ‘Rex Butterhead’. We at the APS Laboratory for Sustainable Food at Florida Gulf Coast University assessed the technical feasibility of growing different leafy green vegetable crops. GREENBOX technology consists of thermally insulated climate-controlled enclosures, an artificial lighting source, a soilless cultivation method (hydroponics), and environmental control modules. We assembled two GREENBOX units to assess the environmental conditions and growth performance of Brassica rapa var. chinensis ‘Li Ren Choi’, Spinach Spinacia oleracea ‘Auroch’, Arugula Eruca sativa ‘Astro’, and Mizuna Brassica Brassica rapa var. japonica. Plugs were cultivated and then transplanted in a randomized manner to the nutrient film technique (NFT) channels, subsequently grown for 30 days to full bloom and ready for harvest. Fertigation was carried out using a standard concentration nutrient solution. Crops were arranged in twelve blocks of four species each. We collected environmental data including daily light integral (DLI, mol/m2∙d), temperature (˚C), relative humidity (%), and vapor pressure deficit (VPD, kPa). Collected biomass data included wet weight (g), dry weight (g), leaf area (cm2), and chlorophyll concentration (mg/cm2). We then derived the Specific Leaf Area (SLA, cm2/g). Descriptive statistics were utilized to understand the differences in biomass parameters between the four crops grown. We also compared the performance parameters of our crops with existing peer-reviewed literature and found it superior, if not comparable to commonly found industrial output. We determined that all crops grew to full bloom, demonstrating that GREENBOX technology may be used to grow a variety of different leafy green vegetable crops.

青藏高原东缘湿地生态系统生物量差异

青藏高原东缘拥有大量的湿地,是我国重要河流的发源地。这一地区湿地的变化会影响我国内陆地区的生态环境。研究地点选取青藏高原东缘的3处典型湿地:若尔盖高原湿地,九寨沟湿地及虹口自然保护区湿地。本文通过对这一地区生物量变化的观测,研究结果发现通过比较,在地上生物量方面进行对比可以发现甘海子和其他3组都与有相关性,且相关性明显(P<0.01)。而其他3组相互之间具有显著差异。在地下生物量方面若尔盖地区的数据和其他3个地区具有显著相关性(P<0.05)。高海拔地区的生物量要比低海拔地区的生物量要高。甘海子和九寨沟的距离极为接近,但甘海子的地上生物量却是九寨沟湿地的2倍(F=9.05,P<0.01)。而甘海子和九寨的的地下生物量没有显著性差异。在固碳效果方面甘海子湿地>若尔盖湿地>九寨沟湿地>虹口保护区。湿地类型是影响生物量变化的主要因素,其次是人类活动。

On Conditional Probabilities of Factoring Quadratics

Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are selected randomly without restriction, the probability that a factorization exists is zero. We achieve a specific quantification of the probability of factoring quadratics by taking a new approach that considers the absolute size of coefficients to be a parameter n. This restriction allows us to make relative likelihood estimates based on finite sample spaces. Our probability estimates are then conditioned on the size parameter n and the behavior of the conditional estimates may be studied as the parameter is varied. Specifically, we enumerate how many formal factored expressions could possibly correspond to a quadratic for a given size parameter. The conditional probability of factorization as a function of n is just the ratio of this enumeration to the total number of possible quadratics consistent with n. This approach is patterned after the well-known case where factorizations are carried out over a finite field. We review the finite field method as background for our method of dealing with Z [x]. The monic case is developed independently of the general case because it is simpler and the resulting probability estimating formula is more accurate. We conclude with a comparison of our theoretical probability estimates with exact data generated by a computer search for factorable quadratics corresponding to various parameter values.

Distribution and Accumulation of Soil Carbon in Temperate Wetland, Northeast China

Estimating carbon sequestration and nutrient accumulation rates in Northeast China are important to assess wetlands function as carbon sink buffering greenhouse gas increasing in North Asia. The objectives of this study were to estimate accreting rates of carbon and nutrients in typical temperate wetlands. Results indicated that average soil organic carbon(SOC), total nitrogen(TN) and total phosphorus(TP) contents were 37.81%, 1.59% and 0.08% in peatlands, 5.33%, 0.25% and 0.05% in marshes, 2.92%, 0.27% and 0.10% in marshy meadows, respectively. Chronologies reconstructed by 210 Pb in the present work were acceptable and reliable, and the average time to yield 0–40 cm depth sediment cores was 150 years. Average carbon sequestration rate(Carbonsq), nitrogen and phosphorus accumulation rates were 219.4 g C/(m^2·yr), 9.16 g N/(m^2·yr) and 0.46 g P/(m^2·yr) for peatland; 57.13 g C/(m^2·yr), 5.42 g N/(m^2·yr) and 2.16 g P/(m^2·yr) for marshy meadow; 78.35 g C/(m^2·yr), 8.70 g N/(m^2·yr) and 0.71 g P/(m2·yr) for marshy; respectively. Positive relations existed between Carbonsq with nitrogen and precipitations, indicating that Carbonsq might be strengthened in future climate scenarios.

On Irrational Points in the Plane

This paper summarizes research intended to develop a pedagogically friendly argument that establishes the fact that (x,ex ) is never a rational point in the plane. A point (x, y)∈R2 is rational if both x and y are rational. Applying a method based on Hurwitz polynomials, the research establishes simple irrationality proofs for nonzero rational powers of e and logarithms of positive rationals (excluding one).

Agricultural Water Conservation in the High Plains Aquifer and Arikaree River Basin

Yuma County is the top crop producing County in Colorado that is dependent on groundwater supplies from the High Plains aquifer for irrigation. The Arikaree River, a tributary of the Republican River in eastern Colorado, is supplied with water from the High Plains aquifer. The Arikaree River alluvium is also a habitat for many terrestrial invertebrates and the threatened Hybognathus hankinsoni (Brassy Minnow). The constant demand on the High Plains aquifer has created declining water levels at the linear rate of 0.183 m/year with the deepest pool in the Arikaree River drying up in 8 to 12 years. In addition to the demands for habitats, the surrounding irrigated agricultural lands require water for crop production. These challenges are currently confronting farmers in eastern Colorado and this research presents possible alternatives to meet these demands. This research presents a combination water balance model, water conservation model, and water conservation survey results from farmers in eastern Colorado to identify alternatives to extend the life of the Arikaree River. The first alternative was to examine the reduction in irrigation water from removing the 18 alluvial irrigation wells that could extend the Arikaree River pools from drying up for 30 years. The other scenario found that water conservation practices with participation of 43%, 57%, and 62% of farmers would extend the drying time to 20, 30, and 40 years, respectively. The final alternative studied was the required participation in conservation practices to stop the decline of the High Plains Aquifer. The analysis found that 77% participation of farmers in all conservation alternatives or reducing pumping by 62.9% would be necessary to stabilize the High Plains Aquifer.

A Geometric Proof of Fermat’s Little Theorem

We present an intuitively satisfying geometric proof of Fermat's result for positive integers that for prime moduli p, provided p does not divide a. This is known as Fermat’s Little Theorem. The proof is novel in using the idea of colorings applied to regular polygons to establish a number-theoretic result. A lemma traditionally, if ambiguously, attributed to Burnside provides a critical enumeration step.

Factorization Patterns in Fq [x]

The finite field Fq has q elements, where q = pk for prime p and k∈N. Then Fq[x] is a unique factorization domain and its polynomials can be bijectively associated with their unique (up to order) factorizations into irreducibles. Such a factorization for a polynomial of degree n can be viewed as conforming to a specific template if we agree that factors with higher degree will be written before those with lower degree, and factors of equal degree can be written in any order. For example, a polynomial f(x) of degree n may factor into irreducibles and be written as (a)(b)(c), where deg a ≥ deg b ≥deg c. Clearly, the various partitions of n correspond to the templates available for these canonical factorizations and we identify the templates with the possible partitions. So if f(x) is itself irreducible over Fq, it would belong to the template [n], and if f(x) split over Fq, it would belong to the template [n] Our goal is to calculate the cardinalities of the sets of polynomials corresponding to available templates for general q and n. With this information, we characterize the associated probabilities that a randomly selected member of Fq[x] belongs to a given template. Software to facilitate the investigation of various cases is available upon request from the authors.

Pringsheim Convergence and the Dirichlet Function

Double sequences have some unexpected properties which derive from the possibility of commuting limit operations. For example, may be defined so that the iterated limits and exist and are equal for all x, and yet the Pringsheim limit does not exist. The sequence is a classic example used to show that the iterated limit of a double sequence of continuous functions may exist, but result in an everywhere discontinuous limit. We explore whether the limit of this sequence in the Pringsheim sense equals the iterated result and derive an interesting property of cosines as a byproduct.

Structured Shuffles and the Josephus Problem

The Australian Shuffle consists of placing a deck of cards onto a table according to this rule: put the top card on the table, the next card on the bottom of the deck, and repeat until all the cards have been placed on the table. A natural question is “Where was the very last card placed located in the original deck?” Card trick magicians have known empirically for years that the fortieth card from the top of a standard fifty-two card deck is the final card placed by this shuffle. The moniker “Australian” comes from putting every other card “Down Under”. We develop a formula for the general case of N cards, and then extend that generalization further to cases involving the discard of k cards before or after putting one on the bottom of the deck. Finally, we discuss the connection of the Australian Shuffle and its generalizations to the famous Josephus problem.

Markov Models for the Tipsy Cop and Robber Game on Graph

In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for different biological scenarios. The first scenario is when the cop and robber have a consistent tipsiness level through the duration of the game;the second is when the cop and robber sober up as a function of time;the third is when the cop and robber sober up as a function of the distance between them. Using Markov chains to model each scenario we calculate the probability of a game persisting through M rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.

On (t, r) Broadcast Domination of Directed Graphs

A dominating set of a graph G is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of G is the order of a minimum dominating set of G. The (t, r) broadcast domination is a generalization of domination in which a set of broadcasting vertices emits signals of strength t that decrease by 1 as they traverse each edge, and we require that every vertex in the graph receives a cumulative signal of at least r from its set of broadcasting neighbors. In this paper, we extend the study of (t, r) broadcast domination to directed graphs. Our main result explores the interval of values obtained by considering the directed (t, r) broadcast domination numbers of all orientations of a graph G. In particular, we prove that in the cases r = 1 and (t, r) = (2, 2), for every integer value in this interval, there exists an orientation of G which has directed (t, r) broadcast domination number equal to that value. We also investigate directed (t, r) broadcast domination on the finite grid graph, the star graph, the infinite grid graph, and the infinite triangular lattice graph. We conclude with some directions for future study.