On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules

Let $(R,\frak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $N$ a finitely generated $R$-module. Let $k{\ge}-1$ be an integer and r=\depth_k(I,N) the length of a maximal $N$-sequence in dimension $>k$ in $I$ defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536). For a subset S\subseteq \Spec R we set S_{{\ge}k}={\p\in S\mid\dim(R/\p){\ge}k}. We first prove in this paper that \Ass_R(H^j_I(N))_{\ge k} is a finite set for all $j{\le}r$}. Let \fN=\oplus_{n\ge 0}N_n be a finitely generated graded \fR-module, where \fR is a finitely generated standard graded algebra over $R_0=R$. Let $r$ be the eventual value of \depth_k(I,N_n). Then our second result says that for all $l{\le}r$ the sets \bigcup_{j{\le}l}\Ass_R(H^j_I(N_n))_{{\ge}k} are stable for large $n$.Comment: To appear in Communication in Algebr

On the cofiniteness of generalized local cohomology modules

Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$ and $M$, $N$ two finitely generated $R$-modules. The aim of this paper is to investigate the $I$-cofiniteness of generalized local cohomology modules \displaystyle H^j_I(M,N)=\dlim\Ext^j_R(M/I^nM,N) of $M$ and $N$ with respect to $I$. We first prove that if $I$ is a principal ideal then $H^j_I(M,N)$ is $I$-cofinite for all $M, N$ and all $j$. Secondly, let $t$ be a non-negative integer such that \dim\Supp(H^j_I(M,N))\le 1 \text{for all} j Then $H^j_I(M,N)$ is $I$-cofinite for all $j<t$ and \Hom(R/I,H^t_I(M,N)) is finitely generated. Finally, we show that if $\dim(M)\le 2$ or $\dim(N)\le 2$ then $H^j_I(M,N)$ is $I$-cofinite for all $j$.Comment: 16 page

Diversity of the genus Sargassum (Fucales: Sargassaceae) in Tho Chu Archipelago, Kien Giang Province.

Our study investigated 12 study sites in four main islands of Tho Chu archipelago in 2019. Six Sargassum species were recorded for the flora of Tho Chu Archipelago, viz.Sargassum aquifolium (Turner) C.Agardh, Sargassum feldmannii Pham-Hoang Ho, Sargassum ilicifolium (Turner) C.Agardh, Sargassum mcclurei Setchell, Sargassum oligocystum Montagne, Sargassum polycystum C.Agardh, among which  three species, namely Sargassum oligocystum Montagne, Sargassum feldmannii Pham-Hoang Ho and Sargassum mcclurei Setchell were newly recorded for Vietnam. There was a significant difference in species composition between Tho Chu, Hon Xanh, Hon Tu and Hon Cao islands; among them, Hon Xanh island differed from the other three islands by 28%, Hon Tu island and Tho Chu island were mostly similarity in flora composition with the similarity index of 85.7%. The morphology of some Sargassum species varied by ecological characteristics, especially for Sargassum aquifolium (Turner) C. Agardh and Sargassum oligocystum Montagne.

SYNTHESIS AND ELECTROCHEMICAL PROPERTIES OF MESOPOROUS CARBON SUPPORTED WELL–DISPERSED COBALT OXIDES NANOPARTICLES

In this article, well–dispersed cobalt oxide nanoparticles supported on mesoporous carbon (CMK–3) have been successfully synthesized. The composites were characterized by field emission scanning electron microscopy, transmission electron microscopy, X–ray diffraction and nitrogen adsorption–desorption analysis. The results have confirmed that, at a cobalt loading of 15 wt%, the composites have not only retained mesoporous structure of the support but also shown a good control of dispersed cobalt oxide nanoparticles with size of ~4 nm. The electrochemical property tests for the synthesized samples have shown significant improvement compared to the blank carbon (CMK–3) without cobalt oxide incorporation

Seaweed diversity in Vietnam, with an emphasis on the brown algal genus Sargassum

Vietnam, a country in South-East Asia, is characterized by a coastline nearly 3300 km long. The coast; stretching from Gulf of Tonkin in the North to the gulf of Thailand in the South, has a predominant North-South orientation resulting in a rich and varied coastal environment. The people in Vietnam have traditionally relied on the rich coastal resources, first by harvesting natural populations and more recently by implementing aquaculture practices. Next to fish and shellfish, marine seaweeds (macroalgae) have traditionally been harvested among most of the Vietnamese coast. A survey of the uses of Vietnamese seaweeds results in 82 species which are considered economically valuable (Chapter 1). Many of these seaweeds are used for human consumption, while others have a role in traditional medicine or are used for colloid extraction (e.g. agar, carrageenan) or as feed for animals. Contrary however to neighboring countries such as China, the Philippines and Indonesia where seaweed mariculture has been seriously developed over the last decades, culturing seaweeds remains a largely marginal activity in Vietnam. Reasons as to why seaweed mariculture has not taken off as compared to the neighboring countries are at least partly to be found in the absence of a phycolloid industry in Vietnam. Instead Vietnam exports large amounts of raw seaweeds, harvested from natural populations, at a low price, and then imports the purified phycocolloids at a much higher price. A steadily growing demand for seaweed-derived products results in an increasing pressure on coastal ecosystems which risk overharvesting of natural populations. This risk is especially eminent for the brown algal genus Sargassum of which approximately 50.000 wet tons is harvested every year. Sargassum represents an important ecosystem engineering species of subtidal coastal habitats. The plants can grow easily up to 3-4 m in length and form dense vegetations with a major nursery function for countless juvenile vertebrate and invertebrate species. If plants, the uprights at least are annual, are harvested before becoming fertile, this may reduce the rejuvenation of natural populations and eventually lead to habitat degradation. Despite the value of seaweeds for humans as well as their role in coastal ecosystems in Vietnam, relatively little is known about them. Basic information on for example the number of species present and their distributions is not easily available. Most information on seaweeds is scattered in local literatures, written in Vietnamese. Thereto, we compiled a checklist of Vietnamese seaweeds (Chapter 2). A total of 827 species are reported (412 Rhodophyta, 180 Chlorophyta, 147 Phaeophyceae, 88 Cyanobacteria. This species richness is comparable to that of the Philippines and considerably higher than Taiwan, Thailand or Malaysia. A comparison of the species composition with neighbouring countries yielded surprisingly low similarities. Rather than an indication of a biogeographical pattern, we are of the opinion that the low similarity with neighboring countries is primarily an artifact resulting from taxonomic inconsistencies. The checklist could serve as a valuable tool, to reveal the seaweed diversity in Vietnam and to stimulate intraregional comparative research. Sargassum with 70 species and intraspecific taxa is undoubtedly the most species-rich seaweed genus in Vietnam (Chapter 3). The estimate of Sargassum diversity is however entirely based on interpretations of the morphological characters such as the base, secondary axes, the leaves, vesicles and receptacles. Therefore we reassessed Sargassum diversity based on molecular gene sequence data of the internal spaces of the ribosomal cistron (ITS rDNA) (Chapter 4). Although successful at higher taxonomic levels, subgenera and sections, the resolution of the ITS marker was not sufficient to point species boundaries with confidence. Many morphologically distinct ‘species’ were characterized by virtually identical ITS sequences. Conversely, specimens identified on morphological criteria as one ‘species’ were resolved in different clades. Results could be interpreted in two possible ways. First, traditional species concepts in Sargassum have been too broadly defined and the genus contains far less species. Alternatively, species in Sargassum result from a recent radiation and even the highly variable ITS region does not display enough variation to resolve the relationship among them. To address these outstanding questions we explored to use of Restriction site Associated DNA Sequences (RAD-Seq) to generate a set of highly variable nuclear markers. RAD-sequencing is a Next Generation Sequencing-based technique that generates thousands to hundreds of thousands DNA fragments that can be scored for Single Nucleotide Polymorphisms (SNPs) which in turn can be compared between individuals. RAD markers can be used to pinpoint loci under selection, or are used as neutral markers to reconstruct phylogeographical patterns or elucidate phylogenetic relationships among closely related species. During the experiment we generated more than 21 million sequences which after quality control and analyses in Stacks and SiLiX yielded 231 alignments which could potentially be used to address species boundaries in the genus Sargassum. The development of more than 200 markers presents a more than significant increase over markers used in traditional studies which generally combine one or two mitochondrial and/or chloroplast markers with sequences from the ribosomal cistron. It also boosts the number of potential markers by a factor 10 to 20 compared to microsatellite-based studies. Despite these results, there are issues that remain to be solved. For example, the libraries of the individual specimens are highly unequal in size. Some specimens are represented by 1.5 million sequences while others only have barely 800 sequences. We believe the main reason why some specimens are underrepresented is due to insufficient DNA quality. Therefore, future studies should focus on obtaining high quality DNA from Sargassum. A second issue is posed by the presence of multiple alleles in the final alignments. Normally one would expect 2 alleles per marker for a diploid organism. Our final alignments often contain more than 2 alleles per specimen. It is unclear at present if this is a technical issue which could eventually be solved by fine-tuning the parameters of the Stacks analyses or whether the multiple alleles issue has an underlying biological cause (polyploidisation). Despite these issues, RAD Sequencing has a great potential for population based molecular studies in algae. A selection of the current stacks can be used for primer design which can then be used to score markers by PCR followed by traditional Sanger sequencing. This approach can easily increase the number of nuclear markers for phylogeographic or species delimitation studies by a factor ten. Modest as it may be, I hope that by providing a compilation of the seaweed diversity in Vietnam and their economical importance, and by introducing DNA-based methodologies to assess species diversity in the ecologically and economically important genus Sargassum, I have contributed to the foundation for a sustainable exploitation of natural resources and continuous integrity of marine habitats

Rice cultivation and soil properties as affected by Alternative Wetting and Drying irrigation in Chau Thanh, An Giang province

The study that was carried out in winter-spring 2018 in Thoai Son, An Giang province, include experiments: Effects of (AWDI) to (i) Characters in soil; (ii) rice yield and (iii) water use and water use efficiency of Jasmine rice. The experiment was carried out with 4 treatments, 4 replications. The treatments ranged from continuous submergence (NT1) of the field to a number of delayed irrigations (NT2, NT3, NT4) denoting application of 4 cm irrigation water when water level in the perforated PVC pipe fell 18, 14 and 10 cm below ground level. The study revealed that NT1 attributed by the highest total water use (118 cm) and the lowest WUE (60.3 kg/ha/cm) produced the highest grain yield (8,10 t/ha). On the contrary, the yields in NT3 (6.80 t/ha) and NT2 (5.80 t/ha) were significantly lower at 0,5 times level of significance compared to that of NT1 and NT4 (7.83 t/ha)

With exhaustible resources, can a developing country escape from the poverty trap ?

This paper studies the optimal growth of a developing non-renewable natural resource producer, which extracts the resource from its soil and produces a single consumption good with man-made capital. Moreover, it can sell the extracted resource abroad and use the revenues to buy an imported good, which is a perfect substitute of the domestic consumption good. The domestic technology is convex-concave, so that the economy may be locked into a poverty trap. We study the optimal extraction and depletion of the exhaustible resource and the optimal paths of accumulation of capital and of domestic consumption. We show that the extent to which the country will optimally escape from the poverty trap and the exhaustible resource will be a blessing depends on the characteristics of its technology and of the revenues from the resource function, on its impatience, on the level of its initial stock of capital and on the abundance of the natural resource. If the marginal productivity of capital at the origin is greater than the sum of the social discount rate and the depreciation rate, the country will accumulate capital along the entire growth path and will escape from the poverty trap, whatever its initial stocks of capital and resource, and provided that the marginal revenue obtained from the exportation of the resource is finite at the origin. On the contrary, if the marginal productivity of capital is lower than the depreciation rate whatever the level of capital and if moreover the initial stock of capital is small, then the country will never accumulate ; it will consume the revenues obtained from selling abroad the extracted resource, until there is no resource left and the economy collapses. We also show that any optimal path may be decentralized in a competitive equilibrium by using a tax/subsidy scheme for firms.Optimal growth, exhaustible resource, convex-concave technology, poverty trap, competitive equilibrium with tax/subsidy.