The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page

Methods of Statistical Control for Groundwater Quality Indicators

The article describes the results of conducted groundwater quality control. Controlled quality indicators included the following microelements - barium, manganese, iron, mercury, iodine, chromium, strontium, etc. Quality control charts - X-bar chart and R chart - were built. For the upper and the lower threshold limits, maximum permissible concentration of components in water and the lower limit of their biologically significant concentration, respectively, were selected. The charts analysis has shown that the levels of microelements content in water at the area of study are stable. Most elements in the underground water are contained in concentrations, significant for human organisms consuming the water. For example, such elements as Ba, Mn, Fe have concentrations that exceed maximum permissible levels for drinking water

Association between cognitive function and supplementation with omega-3 PUFAs and other nutrients in ≥ 75 years old patients: A randomized multicenter study

A few studies have assessed the association between omega-3 polyunsaturated fatty acids (n-3 PUFA) and cognitive impairment (CI) in very old adults. The aim of this study was to evaluate the effect of a multinutrient supplementation rich in n-3 PUFA on the cognitive function in an institutionalized ≥75-year-old population without CI or with mild cognitive impairment (MCI). A multicenter placebo-controlled double-blind randomized trial was conducted between 2012 and 2013. Cognitive function was assessed at baseline and after one year using 4 neuropsychological tests. Nutritional status was assessed using Mini Nutritional Assessment (MNA). Interaction between Mini-Mental State Examination (MMSE) score and nutritional status were analyzed using linear regression models. A total of 99 participants were randomized to receive placebo or pills rich in n-3 PUFA. After 1-year follow-up, both groups decreased their MMSE score (-1.18, SD:0. 53 and -0.82, SD:0. 63, p = 0.67 for the control and the intervention group respectively). The memory subscale of the MMSE showed an improvement (+0.26, SD:0.18) in the intervention group against a worsening in the control group (-0.11, SD: 0.14; p = 0.09 for differences between groups). Patients at intervention group with normal nutritional status (MNA ≥24) showed an improvement in the MMSE (+1.03, p = 0.025 for differences between 1-y and baseline measurements) against a worsening in the group with malnutrition (MNA<24) (-0.4, p = 0.886 for differences between 1-y and baseline; p of interaction p = 0.05). Supplementation with n-3 PUFA did not show an improvement in the global cognitive function in institutionalized elderly people without CI or with MCI. They only suggest an apparent improvement in memory loss if previously they were well nourished

Contrasting tree-cover loss and subsequent land cover in two neotropical forest regions: sample-based assessment of the Mexican Yucatán and Argentine Chaco

The neotropical-forest’s northern and southern extremes, covering the Mexican Yucatán and the Argentine Chaco, have among the highest rates of recent tree-cover loss in the biome. This study contrasts the character of loss in these regions, estimating proportions of types of loss and subsequent land cover. It is based on two-stage probability sampling design and field and satellite-image surveys. All estimates include uncertainties, which could be further reduced via model-assisted estimation or additional sampling. This approach can be replicated in other regions to estimate types of loss and associated land cover from a definitive, in-situ perspective. The character of loss in the two areas differed greatly. That in the Yucatán was 54% temporary, mostly under fallow or selectively logged, while that in the Chaco was 85% permanent, split nearly equally between crops and pasture. These data contribute to a quantitative basis for studies of socio-economic drivers of neotropical deforestation.Fil: Krylov, Alexander. University of Maryland; Estados UnidosFil: Steininger, Marc K.. University of Maryland; Estados UnidosFil: Hansen, Matthew C.. University of Maryland; Estados UnidosFil: Potapov, Peter V.. University of Maryland; Estados UnidosFil: Stehman, Stephen V.. State University of New York; Estados UnidosFil: Gost, Allison. University of Maryland; Estados UnidosFil: Noel, Jacob. University of Maryland; Estados UnidosFil: Talero Ramirez, Yamile. University of Maryland; Estados UnidosFil: Tyukavina, Alexandra. University of Maryland; Estados UnidosFil: Di Bella, Carlos Marcelo. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Ellis, Edward A.. Universidad Veracruzana; MéxicoFil: Ellis, Peter. The Nature Conservancy. Global Lands; Estados Unido