Antibacterial Effects of Flavonoids and Their Structure-Activity Relationship Study: A Comparative Interpretation

According to the latest report released by the World Health Organization, bacterial resistance to well-known and widely available antibacterial drugs has become a significant and severe global health concern and a grim challenge to tackle in order to cure infections associated with multidrug-resistant pathogenic microorganisms efficiently. Consequently, various strategies have been orchestrated to cure the severe complications related to multidrug-resistant bacteria effectively. Some approaches involved the retardation of biofilm formation and multidrug-resistance pumps in bacteria as well as the discovery of new antimicrobial agents demonstrating different mechanisms of action. In this regard, natural products namely alkaloids, terpenoids, steroids, anthraquinone, flavonoids, saponins, tannins, etc., have been suggested to tackle the multidrug-resistant bacterial strains owing to their versatile pharmacological effects. Amongst these, flavonoids, also known as polyphenolic compounds, have been widely evaluated for their antibacterial property due to their tendency to retard the growth of a wide range of pathogenic microorganisms, including multidrug-resistant bacteria. The hydroxylation of C5, C7, C3′, and C4′; and geranylation or prenylation at C6 have been extensively studied to increase bacterial inhibition of flavonoids. On the other hand, methoxylation at C3′ and C5 has been reported to decrease flavonoids’ antibacterial action. Hence, the latest information on the antibacterial activity of flavonoids is summarized in this review, with particular attention to the structure–activity relationship of this broad class of natural compounds to discover safe and potent antibacterial agents as natural products.     

Biofortification—A Frontier Novel Approach to Enrich Micronutrients in Field Crops to Encounter the Nutritional Security

Globally, many developing countries are facing silent epidemics of nutritional deficiencies in human beings and animals. The lack of diversity in diet, i.e., cereal-based crops deficient in mineral nutrients is an additional threat to nutritional quality. The present review accounts for the significance of biofortification as a process to enhance the productivity of crops and also an agricultural solution to address the issues of nutritional security. In this endeavor, different innovative and specific biofortification approaches have been discussed for nutrient enrichment of field crops including cereals, pulses, oilseeds and fodder crops. The agronomic approach increases the micronutrient density in crops with soil and foliar application of fertilizers including amendments. The biofortification through conventional breeding approach includes the selection of efficient genotypes, practicing crossing of plants with desirable nutritional traits without sacrificing agricultural and economic productivity. However, the transgenic/biotechnological approach involves the synthesis of transgenes for micronutrient re-translocation between tissues to enhance their bioavailability. Soil microorganisms enhance nutrient content in the rhizosphere through diverse mechanisms such as synthesis, mobilization, transformations and siderophore production which accumulate more minerals in plants. Different sources of micronutrients viz. mineral solutions, chelates and nanoparticles play a pivotal role in the process of biofortification as it regulates the absorption rates and mechanisms in plants. Apart from the quality parameters, biofortification also improved the crop yield to alleviate hidden hunger thus proving to be a sustainable and cost-effective approach. Thus, this review article conveys a message for researchers about the adequate potential of biofortification to increase crop productivity and nourish the crop with additional nutrient content to provide food security and nutritional quality to humans and livestock.     

Multi-scale Fractured Coal Gas–Solid Coupling Model and Its Applications in Engineering Projects

With coal mining entering the geological environment of “high stress, rich gas, strong adsorption and low permeability,” the difficulty of joint coal and gas extraction clearly augments, the risk of solid–gas coupling dynamic disasters greatly increases, and the underlying mechanisms become more complex. In this paper, based on the characteristics of coal’s multi-scale structure and spatiotemporal variation, the multi-scale fractured coal gas–solid coupling model (MSFM) was built. In this model, the interaction between coal matrix and its fractures and the mechanical characteristics of gas-bearing coal were considered, as well as their coupling relationship. By MATLAB software, the stress–damage–seepage numerical computation programs were developed, which were applied into Comsol Multiphysics to simulate gas flow caused by coal mining. The simulation results showed the spatial variability of coal elastic modulus and cross-flow behaviors of coal seam gas, which were superior to the results of traditional gas–solid coupling model. And the numerical results obtained from MSFM were closer to the measured results in field, while the computation results of traditional model were slightly higher than the measured results. Furthermore, the MSFM in a large scale was verified by field engineering project.     

Weak Morrey spaces and strong solutions to the Navier-Stokes equations

We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p ＞ 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1＜p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results.     

Algorithms with high order convergence speed for blind source extraction

A rigorous convergence analysis for the fixed point ICA algorithm of Hyvärinen and Oja is provided and a generalization of it involving cumulants of an arbitrary order is presented. We consider a specific optimization problem OP(p), p>3, integer, arising from a Blind Source Extraction problem (BSE) and prove that every local maximum of OP(p) is a solution of (BSE) in sense that it extracts one source signal from a linear mixture of unknown statistically independent signals. An algorithm for solving OP(p) is constructed, which has a rate of convergence p?1.     

One-Point Extensions of t-Koszul Algebras

We introduce the category of t-fold modules which is a full subcategory of graded modules over a graded algebra. We show that this subcategory and hence the subcategory of t-Koszul modules are both closed under extensions and cokernels of monomorphisms. We study the one-point extension algebras, and a necessary and sufficient condition for such an algebra to be t-Koszul is given. We also consider the conditions such that the category of t-Koszul modules and the category of quadratic modules coincide.     

Pole placement controllers for linear time-delay systems with commensurate point delays

This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delaydependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is maintained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer‘s choice of a (delay-dependent) arbitrary spectrum assignment objective.     

The duality between Morrey spaces and its pre-dual spaces characterized by heat kernel

Let L be an elliptic operator, we give arguments about the duality estimate between Morrey spaces and its pre-dual spaces characterized by the heat kernel associated to L that is given in [6],[8].     

The interior proximal extragradient method for solving equilibrium problems

In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms.     

Evolution of hypersurfaces by the mean curvature minus an external force field

In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.