A generalization of the finiteness problem of the local cohomology modules

Let R be a commutative Noetherian ring and \(\mathfrak{a}\) an ideal of R. We introduce the concept of \(\mathfrak{a}\) -weakly Laskerian R-modules, and we show that if M is an \(\mathfrak{a}\) -weakly Laskerian R-module and s is a non-negative integer such that Ext _R ^j \((R/\mathfrak{a},H_\mathfrak{a}^i (M))\) is \(\mathfrak{a}\) -weakly Laskerian for all i < s and all j, then for any \(\mathfrak{a}\) -weakly Laskerian submodule X of \(H_\mathfrak{a}^s (M)\) , the R-module \(Hom_R (R/\mathfrak{a},H_\mathfrak{a}^s (M)/X)\) is \(\mathfrak{a}\) -weakly Laskerian. In particular, the set of associated primes of \(H_\mathfrak{a}^s (M)/X\) is finite. As a consequence, it follows that if M is a finitely generated R-module and N is an \(\mathfrak{a}\) -weakly Laskerian R-module such that \(H_\mathfrak{a}^i (N)\) (N) is \(\mathfrak{a}\) -weakly Laskerian for all i < s, then the set of associated primes of \(H_\mathfrak{a}^s (M,N)\) (M,N) is finite. This generalizes the main result of S. Sohrabi Laleh, M.Y. Sadeghi, and M.Hanifi Mostaghim (2012).     

An experimental study on particle formation in emulsifier-free emulsion polymerization of styrene

Particle formation in polymerization of styrene induced within two stratified layers of a monomer and water containing an initiator was studied in the absence of emulsifiers and stirring. A polymerization-induced decrease of interfacial surface tension was observed. The particle size distribution was characterized by dynamic light scattering during polymerization. The results confirm particle nucleation through spontaneous emulsification process.     

The $$\varvec{N}$$ N -soliton,fusion, rational and breather solutions of two extensions of the (2+1)-dimensional Bogoyavlenskii–Schieff equation

Nonlinear Dynamics - The aim of this work is to analyze and explore the dynamics of two extensions of the Bogoyavlenskii–Schieff equation. The Hirota bilinear method is applied to the...     

On coLaskerian module and local cohomology

The notion of generalized Laskerian modules was introduced recently by the authors. In this paper, we continue our investigation of such modules. Moreover, we are going to generalize some results on finiteness of associated primes of local cohomology modules to the category of generalized Laskerian modules.     

Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis

Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime. In this research, we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water waves. We extend the modified expansion function method (MEFM) to obtain abundant solutions, as well as to find new solutions. By using this newly modified method one can obtain novel and more analytic solutions comparing to MEFM. Also, numerical solutions via the Adomian decomposition scheme are discussed and favorable comparisons with analytical solutions have been done with an outstanding agreement. Besides, the instability modulation of the governing equations are explored through the linear stability analysis function. All new solutions satisfy the main coupled equation after they have been put into the governing equations.     

Crystal Growth of Diazabicyclo[2.2.2]octane-1,4-diium dichromate

Abstract  

The crystal growth of (C₆H₁₄N₂)[Cr₂O₇], consists of a diazabicyclo[2.2.2]octane-1,4-diium cation and a discrete dichromate anion, in solution has been determined under the influence of various factors. Four factors, which influence the crystal size, crystal growth and nucleation, were chosen. These factors are concentration, temperature, type of solvent and method of crystallization. Taguchi design of experiments (DOE) method has been used for to plan a minimum number of experiments and optimization of crystallization processes. Crystallization of diazabicyclo[2.2.2]octane-1,4-diium dichromate with desirable particle size, shape and minimum time of crystal growth as performance characteristics were studied. The changes in the crystal growth habit were observed and could be explained by the differences in the morphology on the various photograph of this compound.     

Analyzing the effects of thermal stress on insulator papers by solid-state 13C NMR spectroscopy

Cellulose - Million tons of cellulosic paper have been used for insulating coils in oil-filled electrical power transformers, thereby assuring the electricity supply for our societies. The high...     

Mild bromination of unreactive aromatic compounds

N,N,N′,N′-Tetrabromobenzene-1,3-disulfonamide and poly(N,N′-dibromo-N-ethylene-benzene-1,3-disulfonamide) in concentrated H₂SO₄ can be used as efficient reagents for the mild bromination of unreactive arenes at room temperature, under solvent-free conditions, in good yields.     

An Efficient Solvent Free Synthesis of 1,8-Dioxo-octahydroxanthene Using p-Toluene Sulfonic Acid

A simple and efficient method for the synthesis of 1,8‐dioxo‐octahydroxanthene by using p‐toluenesulfonic acid as a catalyst under solvent free conditions is described, which involves cyclization of 2,2‐arylmethylenebis(3‐hydroxy‐5,5‐dimethyl‐2‐cyclohexene‐1‐one) that was obtained firstly by the reaction of dimedone with aromatic aldehydes in water as solvent and catalyst at room temperature. The experimental procedures in the two steps are very simple and the products are formed in excellent yields.