Characterization of the Graded Betti Numbers for Almost Complete Intersections

Using standard mapping cone procedure of the inclusion map of an ideal generated by a suitable regular sequence inside a Gorenstein ideal and by a deep analysis of possible cancellations, we give a numerical characterization of the graded Betti sequences admissible for almost complete intersections of height three.     

Partial Regularity of the Minimizers of Quadratic Functionals with VMO Coefficients

The paper investigates the partial regularity of the minimizersfor quadratic functionals whose integrands have VMO coefficientsin principal part and nonlinear terms that are Carathéodoryfunctions. We use some majorizations for the functional, ratherthan the well known Euler equation associated to it.     

Linear growth coefficients in quasilinear equations

In the paper the author proves properties of existence, uniqueness and regularity for divergence form elliptic equations, extending these results from the linear case to the quasilinear one.     

Enhanced Laccase Production in White-Rot Fungus <Emphasis Type="Italic">Rigidoporus lignosus</Emphasis> by the Addition of Selected Phenolic and Aromatic Compounds

The white rot fungus Rigidoporus lignosus produces substantial amounts of extracellular laccase, a multicopper blue oxidase which is capable of oxidizing a wide range of organic substrates. Laccase production can be greatly enhanced in liquid cultures supplemented with various aromatic and phenolic compounds. The maximum enzyme activity was reached at the 21st or 24th day of fungal cultivation after the addition of inducers. The zymograms of extracellular fluid of culture preparation in the presence of inducers, at maximum activity day, revealed two bands with enzymatic activity, called Lac1 and Lac2, having different intensities. Lac2 band shows the higher intensity which changed with the different inducers. Laccase induction can be also obtained by adding to the culture medium olive mill wastewaters, which shows a high content of phenolic compounds     

Commutators and generalized local Morrey spaces

In this paper we study the behavior of Hardy–Littlewood maximal operator and the action of commutators in generalized local Morrey spaces $L{M}_{\{x_0\}}^{p,\phi }({\mathbb{R}}^n)$ and generalized Morrey spaces $M^{p,\phi }({\mathbb{R}}^n)$.     

Equitable specialized block-colourings for 4-cycle systems—I

A block-colouring of a 4-cycle system (V,B) of order v=1+8k is a mapping ?:B→C, where C is a set of colours. Every vertex of a 4-cycle system of order v=8k+1 is contained in blocks and r is called, using the graph theoretic terminology, the degree or the repetition number. A partition of degree r into s parts defines a colouring of type s in which the blocks containing a vertex x are coloured exactly with s colours. For a vertex x and for i=1,2,…,s, let B_x,i be the set of all the blocks incident with x and coloured with the ith colour. A colouring of type s is equitable if, for every vertex x, we have |B_x,i−B_x,j|≤1, for all i,j=1,…,s. In this paper we study bicolourings, tricolourings and quadricolourings, i.e. the equitable colourings of type s with s=2, s=3 and s=4, for 4-cycle systems.     

Tree-Level Violation of the Equivalence Principle

Massive particles of spin 0 and 1 violate the equivalence principle (EP) at the tree level. On the other hand, if these particles are massless, they agree with the EP, which leads us to conjecture that from a semiclassical viewpoint massless particles, no matter what their spin, obey the EP. General relativity predicts a deflection angle of 2.63 for a nonrelativistic spinless massive boson passing close to the Sun, while for a massive vectorial boson of spin 1 the corresponding deflection is 2.62.     

Bioactive Metabolites from Marine Algae as Potent Pharmacophores against Oxidative Stress-Associated Human Diseases: A Comprehensive Review

In addition to cancer and diabetes, inflammatory and ROS-related diseases represent one of the major health problems worldwide. Currently, several synthetic drugs are used to reduce oxidative stress; nevertheless, these approaches often have side effects. Therefore, to overcome these issues, the search for alternative therapies has gained importance in recent times. Natural bioactive compounds have represented, and they still do, an important source of drugs with high therapeutic efficacy. In the “synthetic” era, terrestrial and aquatic photosynthetic organisms have been shown to be an essential source of natural compounds, some of which might play a leading role in pharmaceutical drug development. Marine organisms constitute nearly half of the worldwide biodiversity. In the marine environment, algae, seaweeds, and seagrasses are the first reported sources of marine natural products for discovering novel pharmacophores. The algal bioactive compounds are a potential source of novel antioxidant and anticancer (through modulation of the cell cycle, metastasis, and apoptosis) compounds. Secondary metabolites in marine Algae, such as phenolic acids, flavonoids, and tannins, could have great therapeutic implications against several diseases. In this context, this review focuses on the diversity of functional compounds extracted from algae and their potential beneficial effects in fighting cancer, diabetes, and inflammatory diseases.