Zero Triple Product Determined Matrix Algebras

Let A be an algebra over a commutative unital ring C. We say that A is zero triple product determined if for every C-module X and every trilinear map {⋅,⋅,⋅}, the following holds: if {x,y,z}=0 whenever xyz=0, then there exists a C-linear operator T:A3⟶X such that x,y,z=T(xyz) for all x,y,z∈A. If the ordinary triple product in the aforementioned definition is replaced by Jordan triple product, then A is called zero Jordan triple product determined. This paper mainly shows that matrix algebra Mn(B), n≥3, where B is any commutative unital algebra even different from the above mentioned commutative unital algebra C, is always zero triple product determined, and Mn(F), n≥3, where F is any field with chF≠2, is also zero Jordan triple product determined

Steady-state bifurcation of FHN-type oscillator on a square domain

The Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the D4-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations. In this paper, taking the FHN model as an example, we give a explicit calculation formula of normal form for the simple and double Turing bifurcation of the reaction-diffusion equation with Dirichlet boundary conditions and defined on a square space, and we also obtain a method for the calculation of the existence of spatially inhomogeneous steady-state solutions. This paper provides a theoretical basis for exploring and predicting the pattern formation of spatial multimode interaction

The Stability Criteria with Compound Matrices

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems

Influence of ultrasound-assisted alkali treatment on the structural properties and functionalities of rice protein

peer-reviewedThe poor solubility of rice protein (RP) limits its applications in food industry. In this study, the effects of ultrasound-assisted alkali (UAA) treatment on the solubility, structure and functional properties of RP were investigated. Using UAA treatment, the solubility of RP increased with increasing alkali concentration, reaching a maximum value of 19.79 mg/mL at an alkali concentration of 0.08 M. The solubility was improved by 230-fold compared to un-treated samples. In addition, a reduction in particle size and degradation of the protein subunit were observed. UAA seemed to unfold the protein internal structural conformation and expose buried functional groups, which are linked to good emulsifying properties and foaming properties. A decrease in zeta potential was also observed after UAA treatment, which could be the reason for the decreased stability of the emulsion. UAA treatment modified the protein structure and significantly improved solubility

Phenotypic, fermentation characterization, and resistance mechanism analysis of bacteriophage-resistant mutants of Lactobacillus delbrueckii ssp. bulgaricus isolated from traditional Chinese dairy products

peer-reviewedBacteriophage infection is a large factor in dairy industrial production failure on the basis of pure inoculation fermentation, and developing good commercial starter cultures from wild dairy products and improving the environmental vigor of starter cultures by enhancing their phage resistance are still the most effective solutions. Here we used a spontaneous isolation method to obtain bacteriophage-resistant mutants of Lactobacillus delbrueckii ssp. bulgaricus strains that are used in traditional Chinese fermented dairy products. We analyzed their phenotypes, fermentation characteristics, and resistance mechanisms. The results showed that bacteriophage-insensitive mutants (BIM) BIM8 and BIM12 had high bacteriophage resistance while exhibiting fermentation and coagulation attributes that were as satisfying as those of their respective parent strains KLDS1.1016 and KLDS1.1028. According to the attachment receptor detection, mutants BIM8 and BIM12 exhibited reduced absorption to bacteriophage phiLdb compared with their respective bacteriophage-sensitive parent strains because of changes to the polysaccharides or teichoic acids connected to their peptidoglycan layer. Additionally, genes, including HSDR, HSDM, and HSDS, encoding 3 subunits of a type I restriction-modification system were identified in their respective parent strains. We also discovered that HSDR and HSDM were highly conserved but that HSDS was variable because it is responsible for the DNA specificity of the complex. The late lysis that occurred only in strain KLDS1.1016 and not in strain KLDS1.1028 suggests that the former and its mutant BIM8 also may have an activatable restriction-modification mechanism. We conclude that the L. bulgaricus BIM8 and BIM12 mutants have great potential in the dairy industry as starter cultures, and their phage-resistance mechanism was effective mainly due to the adsorption interference and restriction-modification system

Optimization of ultrasound-microwave synergistic extraction of prebiotic oligosaccharides from sweet potatoes (Ipomoea batatas L.)

peer-reviewedIn this study, efficient ultrasound–microwave-assisted extraction (UMAE) of prebiotic oligosaccharides from sweet potatoes (Ipomoea batatas L.) was investigated. Response surface methodology was used to optimize the extraction conditions: extraction time, ultrasonic power, and microwave power. The prebiotic effect of extracted oligosaccharides on Bifidobacterium adolescentis was also investigated. The results show that the processing conditions of UMAE for optimum the yields of prebiotic oligosaccharides from sweet potatoes (PPOS4 and PPOS5) and corresponding absorbance (OD) are 100 s extraction time, 300 W ultrasonic power, and 200 W microwave power. Under these conditions, the experimental yields of PPOS4 and PPOS5 and the corresponding OD were 1.472%, 5.476%, and 2.966, respectively, which match the predicted values well. Compared with the conventional hot-water extraction (HWE), microwave-assisted extraction (MAE), and ultrasound assisted extraction (UAE) methods, the UMAE procedure exhibited significantly high extraction efficiency (p < 0.05). Comparison of SEM images of tissues of the sweet potatoes after extractions indicate microfractures and disruption of cell walls in the potato tissues. These results confirm that UMAE has great potential and efficiency in the extraction of bioactive substances in the food and medicinal industries

A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field

Let be an arbitrary field and a square matrix over . Then is sum of two square nilpotent matrices over if and only if, for every algebraic extension of and arbitrary nonzero , there exist idempotent matrices and over such that

Using polysaccharides for the enhancement of functionality of foods: A review

peer-reviewedBackground: Flavor, taste and functional ingredients are important ingredients of food, but they are easily lost or react during heating and are not stable. Carbohydrate-carbohydrate interactions (CCIs) and carbohydrate-protein interactions (CPIs) are involved in a variety of regulatory biological processes in nature, including cell differentiation, proliferation, adhesion, inflammation and immune responses. Polysaccharides have high molecular weights and many intramolecular hydrogen bonds, can be easily modified chemically and biochemically to enhance bioadhesive and biostability of tissues. Therefore, polysaccharides are the foundation for building complex and stable biosystems that are non-toxic with highydrophilicity and easily biodegradable. Scope and approach: In this review, we summarize the principles and applications of polysaccharide delivery systems in a variety of foods. Key findings and conclusions: This review focuses on the self-assembly of carbohydrates with complex structures and discusses the latest advances in self-assembly systems. The host-guest complexes formed by polyvalent sugar conjugates have the potential to provide, control or target delivery or release systems. They can also extend the shelf life of food and prevent oxidation and isomerization during food storage. Moreover, very few studies have outlined a comprehensive overview of the use of various types of food polysaccharide matrixes for the assembly and protection of food ingredients, which is a very important area for further study