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Let $(R,\mathfrak {m})$ be a Noetherian local ring, let I be an ideal of R, and let M be a finitely generated R-module with $d=\dim (M)$ . In this paper, we establish shifted principles under localization and completion for attached primes of the top local cohomology module ${H^{d}_{I}}(M).$ We characterize the catenarity, the weak going-up property, and the strong Lichstenbaum-Hartshorne vanishing property of the base ring R in terms of these shifted principles of the top local cohomology modules.

International audience; Development of fast, accurate, mobile and low-cost tools for food analysis is an important topic to mitigate food-borne diseases. In this paper, a portable sensors based on S11 and S21 of compact circularly polarized antennas is proposed. A low-cost and portable VNA analyser is used to perform measurement and analysis. Fruits are used to assess the test-bed capability to classified different species. A raw of measurement using Orange, Tomato and Mango demonstrates that a signature for each species can be extracted. First results show the reflection coefficient isless sensitive than transmission coefficient to fruit position.

Let ( R , m ) be a Noetherian local ring and M a finitely generated R-module. The invariants p ( M ) and sp ( M ) of M were introduced in [3] and [17] in order to measure the non-Cohen–Macaulayness and the non-sequential-Cohen–Macaulayness of M, respectively. Let M = D 0 ⊃ D 1 ⊃ … ⊃ D k be the filtration of M such that D i is the largest submodule of M of dimension less than dim ⁡ D i − 1 for all i ≤ k and p ( D k ) ≤ 1 . In this paper we prove that if sp ( M ) ≤ 1 , then there exists a constant c such that ir M ( q M ) ≤ c for all good parameter ideals q of M with respect to this filtration. Here ir M ( q M ) is the reducibility index of q on M. This is an extension of the main results of [19] , [20] , [24] .

Let ( R , m ) be a Noetherian local ring which is a quotient of a Gorenstein local ring. Let M be a finitely generated R-module and K M the canonical module of M. Denote by nCM ( M ) the non Cohen–Macaulay locus of M. In this paper, the relationship between the two loci nCM ( K M ) and nCM ( M ) is given. The structure of M is clarified in case where dim ⁡ nCM ( K M ) ≤ 0 (i.e. K M is generalized Cohen–Macaulay).

Let $R$ be a Noetherian ring. For a finitely generated $R$-module $M$, Northcott introduced the reducibility index of $M$, which is the number of submodules appearing in an irredundant irreducible decomposition of the submodule $0$ in $M$. On the other hand, for an Artinian $R$-module $A$, Macdonald proved that the number of sum-irreducible submodules appearing in an irredundant sum-irreducible representation of $A$ does not depend on the choice of the representation. This number is called the sum-reducibility index of $A$. In the former part of this paper, we compute the reducibility index of $S\otimes_R M$, where $R\to S$ is a flat homomorphism of Noetherian rings. Especially, the localization, the polynomial extension, and the completion of $R$ are studied. For the latter part of this paper, we clarify the relation among the reducibility index of $M$, that of the completion of $M$, and the sum-reducibility index of the Matlis dual of $M$., 12 pages

Let ( R , m ) be a Noetherian local ring and M a finitely generated R-module. Let P ∈ Spec ( R ˆ ) and p = P ∩ R . Then the natural map R p → R ˆ P is a flat local homomorphism. In this paper, we provide some relations between the two sets of attached primes of the Artinian local cohomology modules H P R ˆ P i + r P ( M p ⊗ R p R ˆ P ) and H p R p i ( M p ) , where i ≥ 0 is an integer and r P = dim ⁡ ( R ˆ P / p R ˆ P ) . Then, we compute the dimension and multiplicity of H P R ˆ P i + r P ( M p ⊗ R p R ˆ P ) in terms of that of H p R p i ( M p ) respectively. As applications, we give connections between the Cohen–Macaulayness in dimension >s of M ˆ P and that of M p , for an integer s ≥ − 1 .

Let M be a finitely generated module over a Noetherian local ring R. In this paper we introduce the notion of sequential polynomial type of M, which is denoted by sp ( M ) , in order to measure how far M is different from the sequential Cohen–Macaulayness. We study the sequential polynomial type under localization and m -adic completion. We investigate an ascent–descent property of sequential polynomial type between M and M / x M for certain parameter x of M. When R is a quotient of a Gorenstein local ring, we describe sp ( M ) in term of the deficiency modules of M.

International audience; This paper proposes a model for building a flexible system, which accepts and verifies the change on business logic, including both business processes and business rules, while the system has to cover the properties as reliability and reuse. In this model, the business process will be designed with Colour Petri Net and translated into a set of Event-Condition-Action rules, this set will be combined with business rules for checking the respect of a business process to the business rules in design and modifying the process. Hierarchical Colour Petri Net is also used to guarantee the reliability and to reuse properties of the system.; Ce document propose un modèle pour la création d'un système flexible, qui accepte et vérifie les modifications apportées à la logique métier, y compris les processus et les règles métier, tandis que le système doit couvrir les propriétés en termes de fiabilité et de réutilisation. Dans ce modèle, le processus de gestion sera conçu avec un réseau Pétri coloré et traduit en un ensemble de règles Event-Condition-Action (ECA). Cet ensemble sera combiné à des règles de gestion permettant de vérifier le respect du processus de gestion par modifier le processus. Un réseau Pétri coloré hiérarchisé est également utilisé pour garantir la fiabilité et pour réutiliser les propriétés du système

International audience; This paper proposes a model for building a flexible system, which accepts and verifies the change on business logic, including both business processes and business rules, while the system has to cover the properties as reliability and reuse. In this model, the business process will be designed with Colour Petri Net and translated into a set of Event-Condition-Action rules, this set will be combined with business rules for checking the respect of a business process to the business rules in design and modifying the process. Hierarchical Colour Petri Net is also used to guarantee the reliability and to reuse properties of the system.; Ce document propose un modèle pour la création d'un système flexible, qui accepte et vérifie les modifications apportées à la logique métier, y compris les processus et les règles métier, tandis que le système doit couvrir les propriétés en termes de fiabilité et de réutilisation. Dans ce modèle, le processus de gestion sera conçu avec un réseau Pétri coloré et traduit en un ensemble de règles Event-Condition-Action (ECA). Cet ensemble sera combiné à des règles de gestion permettant de vérifier le respect du processus de gestion par modifier le processus. Un réseau Pétri coloré hiérarchisé est également utilisé pour garantir la fiabilité et pour réutiliser les propriétés du système

Eryngium foetidum L. has been used as a spice for food and treatment for diabetes, rheumatism, anti-inflammatories, respiratory and stomach disorders. In Vietnam, due to high consumption of Eryngium foetidum L. in popular dishes and its significant benefits, the preliminary screening of the plant phytochemicals is required to extend its application and improve efficacy. The present research aimed at Eryngium foetidum L. extraction using aqueous and ethanolic as solvents to explore their phytochemical composition, total contents of flavonoids and phenolics and antioxidant activity. Phytochemical screening has detected the presence of flavonoids, tannins, alkaloids and terpenoids in both plant extracts. In addition, the total content of phenolics in both extract was equally significant while the total content of flavonoids was higher in ethanolic extract, as compared to the aquaeous extract. The antioxidant actions of aquaeous and ethanolic extracts were estimated using DPPH and ABTS scavenging assays. Results have shown that the former exhibited stronger DPPH scavenging activity than the latter. Findings from the present study suggested that ethanol and water can be useful for Eryngium foetidum L. extraction with high content of phytochemicals, phenolics and antioxidant activity.

Pandanus amaryllifolius Roxb. was commonly used in Vietnam as a fragrance because of its aroma. These aromatic plants are the primary source of medicinal herbs because of their valuable biological activities. This study was aimed at determining the phytochemical content, Total flavonoids contents (TFC), total phenolic content (TPC) and antioxidants were analyzed by Folin-Ciocalteu and DPPH scavenging assays, respectively. The total flavonoid content is measured by the aluminum chloride method. The qualitative phytochemical analysis confirmed the presence of flavonoids, terpenoids, coumarin, and reducing sugar, which is chemical components in Pandanus amaryllifolius Roxb extract. Results showed that ethanol extract exhibited higher DPPH (129.327 ug/ml) and TPC (38.12 mgGAE/DW) activity than water extraction (265.738 ug/ml and 10.97 mgGAE/DW). Research shows that using this plant more in pharmaceuticals or food should be focused and developed.

Coconut oil is considered the active ingredient as a moisturizer used by many people in tropical regions. At the same time, coconut oil can improve the symptoms of skin disorders by moisturizing and soothing the skin. A body washes formula that contains coconut oil based on the saponification process is formulated through an appropriate content survey. The combination of auxiliary substances such as detergent, foaming agent, moisturizing agent, preservative was also conducted to evaluate different concentrations. Products are assessed and visually observed for appearance, viscosity, pH value, stability, and durability when stored. The body wash formula was found to be white and pearl luster was visually observed. Products using 20% crude soap content, 5% detergent (SLES), 3% glycerin, etc. have all been tested to show good physico-chemical properties in terms of pH value and viscosity, as well as no irritation, upon skin contact. Research shows that coconut oil body wash formulas with good physico-chemical properties can be developed into new body wash cosmetic products.

In order to enhance the use of coconut oil through its application in personal care products, shampoos formulated with simple soap act as the leading detergent with a 20% content and ingredients other commercial components such as Sodium Lauryl Ether Sulfate, Plantacare 2000, Glycerin, Cocamidopropyl Betaine, etc. A combination of 20% crude soap and a synthetic active substance synthesizing sodium lauryl ether sulfate (SLES) 5% make up the excellent shampoo recipe with cleansing feature. Ingredients of complementary detergents, moisturizers, and smoothing softeners are supplemented with appropriate levels to improve raw soap’s disadvantages. Foamability and foam durability are selected targets to examine the influence of ingredients in the formula. The sensory elements of the product reach the set goals with an average evaluation score of about 4/5. Thereby, shampoo products penetrate the cosmetic market and attract many consumers in the future.