Some results on the annihilators and attached primes of local cohomology modules

Let \((R, \mathfrak {m})\) be a local ring and M a finitely generated R-module. It is shown that if M is relative Cohen–Macaulay with respect to an ideal \(\mathfrak {a}\) of R, then \({\text {Ann}}_R(H_{\mathfrak {a}}^{{\text {cd}}(\mathfrak {a}, M)}(M))={\text {Ann}}_RM/L={\text {Ann}}_RM\) and \({\text {Ass}}_R (R/{\text {Ann}}_RM)\subseteq \{\mathfrak {p}\in {\text {Ass}}_R M|\,\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})={\text {cd}}(\mathfrak {a}, M)\},\) where L is the largest submodule of M such that \(\mathrm{cd}(\mathfrak {a}, L)< \mathrm{cd}(\mathfrak {a}, M)\). We also show that if \(H^{\dim M}_{\mathfrak {a}}(M)=0\), then \({\text {Att}}_R(H^{\dim M-1}_{\mathfrak {a}}(M))= \{\mathfrak {p}\in {\text {Supp}}(M)|\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\dim M-1\},\) and so the attached primes of \(H^{\dim M-1}_{\mathfrak {a}}(M)\) depend only on \({\text {Supp}}(M)\). Finally, we prove that if M is an arbitrary module (not necessarily finitely generated) over a Noetherian ring R with \(\mathrm{cd}(\mathfrak {a}, M)=\mathrm{cd}(\mathfrak {a}, R/{\text {Ann}}_RM)\), then \({\text {Att}}_R(H^{\mathrm{cd}(\mathfrak {a}, M)}_{\mathfrak {a}}(M))\subseteq \{\mathfrak {p}\in {\text {V}}({\text {Ann}}_RM)|\,\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\mathrm{cd}(\mathfrak {a}, M)\}.\) As a consequence of this, it is shown that if \(\dim M=\dim R\), then \({\text {Att}}_R(H^{\dim M}_{\mathfrak {a}}(M))\subseteq \{\mathfrak {p}\in {\text {Ass}}_R M|\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\dim M\}\).     

Facile Desulfurization of Thioamides and Thioureas with Tetrabutylammonium Periodate under Mild Conditions

Summary. Thioamides and thioureas were reacted with tetrabutylammonium periodate at room temperature to afford the corresponding amides and ureas, respectively, under aprotic conditions.     

A Review on Machine Learning Approaches for Network Malicious Behavior Detection in Emerging Technologies

Network anomaly detection systems (NADSs) play a significant role in every network defense system as they detect and prevent malicious activities. Therefore, this paper offers an exhaustive overview of different aspects of anomaly-based network intrusion detection systems (NIDSs). Additionally, contemporary malicious activities in network systems and the important properties of intrusion detection systems are discussed as well. The present survey explains important phases of NADSs, such as pre-processing, feature extraction and malicious behavior detection and recognition. In addition, with regard to the detection and recognition phase, recent machine learning approaches including supervised, unsupervised, new deep and ensemble learning techniques have been comprehensively discussed; moreover, some details about currently available benchmark datasets for training and evaluating machine learning techniques are provided by the researchers. In the end, potential challenges together with some future directions for machine learning-based NADSs are specified.     

Application of the single comparator method to instrumental photon activation analysis

Journal of Radioanalytical and Nuclear Chemistry - Instrumental photon activation analysis (IPAA) is nondestructive and multi-elemental analysis method like instrumental neutron activation...     

Preparation of CoFe2O4/sawdust and NiFe2O4/sawdust magnetic nanocomposites for removal of oil from the water surface

In this study, CoFe₂O₄/Sawdust and NiFe₂O₄/Sawdust magnetic nanocomposites were synthesized using a hydrothermal method, and then characterized using X-ray powder diffraction, Infrared, scanning electron microscopy, Brunauer–Emmett–Teller/Barrett–Joyner–Halenda, and vibrating-sample magnetometer techniques. In this study, unmodified sawdust (US), modified sawdust (MS), unmodified CoFe₂O₄/sawdust (UCS), modified CoFe₂O₄/sawdust (MCS), unmodified NiFe₂O₄/sawdust (UNS), and modified NiFe₂O₄/Sawdust (MNS) magnetic nanocomposites, which are inexpensive, economical, environmentally friendly absorbents, and have a high selective hydrophobic, were used for the removal of oil from the water surface. The results show that the UCS, MCS, UNS, and MNS magnetic nanocomposites can selectively absorb the oil spreading on the water surface, due to its superhydrophobicity and superoleophilicity, and can be easily collected from water under the influence of a magnetic field. In addition, the results showed that the absorbents reach their equilibrium at the 30-min mark. Among all the absorbents, the MNS magnetic nanocomposite showed the maximum absorption capacity (18.172 g/g) at the 40-min mark. The results of the kinetic studies showed that the second-order kinetic equation with the highest correlation coefficient had the best fit with the experimental results.     

Synthesis and characterization of copper(II) complexes incorporating pyrazolyl-derived N,S-donor bidentate ligands

The novel bidentate N,S-donor anionic ligands [PhNCSIndz]^?, [PhNCSImz]^?, [PhNCSPz^Me3]^?, and [EtNCSPz]^?, where Indz?=?indazole, Imz?=?imidazole, Pz^Me3?=?3,4,5-trimethylpyrazole, and Pz?=?pyrazole, were synthesized and used to prepare Cu(II) complexes of general formula [Cu(N^S)₂]. The ligands were synthesized via direct addition of phenylisothiocyanate or ethylisothiocyanate into THF suspensions of the corresponding sodium-pyrazolate salts. All of the synthesized compounds, including the ligands and the complexes, were characterized by physico-chemical and spectroscopic methods, and crystal structures of [Cu(EtNCSPz)₂] and [Cu(PhNCSPz^Me2)₂] were determined by X-ray diffraction analysis, showing a trans-square planar geometry for [Cu(EtNCSPz)₂] and a distorted tetrahedral geometry for [Cu(PhNCSPz^Me2)₂].     

A novel one-pot synthesis of some new interesting pyrrole derivatives

[reaction: see text] 11-(1H-Pyrrol-1-yl)-11H-indeno[1,2-b]quinoxaline and 3-(1H-pyrrol-1-yl)indolin-2-one derivatives have been synthesized in good yields in a novel, one-pot, and efficient process by condensation of 11H-indeno[1,2-b]quinoxalin-11-one or isatin derivatives with 4-hydroxyproline on solid-support montmorillonite K10 under microwave irradiation.     

Highly Regioselective Ring Opening of Epoxides with Thiols Catalyzed by SbCl3 Under Solvent-Free Conditions

The ring-opening reaction of epoxides with thiols by SbCl ₃ supported on Kieselguhr under solvent-free conditions, afforded high yields of β-hydroxy sulfides. Nucleophilic attack of the thiols occurs regioselectively at the less hindered side of the epoxides.     

KF/Al2O3 as an Efficient,Green, and Reusable Catalytic System for the Solvent-Free Synthesis of N-Alkyl Derivatives of Sulfonamides via Michael Reactions

KF/Al ₂ O ₃ efficiently catalyzes the microwave-assisted Michael addition of sulfonamides to α,β-unsaturated esters under solvent-free conditions to afford N-alkyl derivatives of sulfonamides as biologically interesting compounds in high yields and in short reaction times. In this reaction, N,N-dialkylsulfonamides are also produced, but in very low yields.