A new class of alternative theorems for SOS-convex inequalities and robust optimization

In this paper, we present a new class of alternative theorems for SOS-convex inequality systems without any qualifications. This class of theorems provides an alternative equations in terms of sums of squares to the solvability of the given inequality system. A strong separation theorem for convex sets, described by convex polynomial inequalities, plays a key role in establishing the class of alternative theorems. Consequently, we show that the optimal values of various classes of robust convex optimization problems are equal to the optimal values of related semidefinite programming problems (SDPs) and so, the value of the robust problem can be found by solving a single SDP. The class of problems includes programs with SOS-convex polynomials under data uncertainty in the objective function such as uncertain quadratically constrained quadratic programs. The SOS-convexity is a computationally tractable relaxation of convexity for a real polynomial. We also provide an application of our theorem of the alternative to a multi-objective convex optimization under data uncertainty.     

Varieties of solvable index-two alternative algebras over a field of characteristic three

The subvarieties of the variety Alt₂ of solvable index-two alternative algebras over an arbitrary field of characteristic 3 are studied. The main types of such varieties are singled out in the language of identities, and inclusions between these types are established. The main results is the following.Theorem.The topological rank of the variety Alt₂ of solvable index-two alternative algebras over an arbitrary field of characteristic 3 is equal to five. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 556–566, October, 1999.     

离心压气机下游边界简化替代方法研究

本文研究的压气机轮缘壁面静压在小流量工况下出现了一个非常有趣的现象,在周向形成了高/低交错分布的四个静压条带,被称为静压周向双峰分布形式.为了方便研究静压周向双峰分布的形成机制,提出了一种下游边界的简化替代方法.将复杂的下游边界简化为高静压区域和具有周向压力梯度的区域,去掉蜗壳和出口管道,直接将简化边界条件施加在扩压器...     

Preliminary Study on New Alternative Binders through Re-Refined Engine Oil Bottoms (REOBs) and Industrial By-Product Additives

Recent studies have worked towards addressing environmental issues such as global warming and greenhouse gas emissions due to the increasing awareness of the depletion of natural resources. The asphalt industry is seeking to implement measures to reduce its carbon footprint and to promote sustainable operations. The reuse of several wastes and by-products is an example of a more eco-friendly activity that fulfils the circular economy principle. Among all possible solutions, the road pavement sector encourages, on one hand, the use of recycled materials as a partial replacement of the virgin lithic skeleton; on the other hand, it promotes the use of recycled materials to substituting for a portion of the petroleum bituminous binder. This study aims to use Re-refined Engine Oil Bottoms (REOBs) as a main substitute and additives from various industrial by-products as a full replacement for virgin bitumen, producing high-performing alternative binders. The REOBs have been improved by utilizing additives in an attempt to improve their specific properties and thus to bridge the gap between REOBs and traditional bituminous binders. An even larger amount of virgin and non-renewable resources can be saved using these new potential alternative binders together with the RAP aggregates. Thus, the reduction in the use of virgin materials is applied at the binder and the asphalt mixture levels. Rheological, spectroscopic, thermogravimetric, and mechanical analysis were used to characterize the properties, composition, and characteristics of the REOBs, REOB-modified binders, and asphalt mixes. Thanks to the rheological investigations of possible alternative binders, 18 blends were selected, since they behaved like an SBS-modified bitumen, and then they were used for producing the corresponding asphalt mixtures. The preliminary mechanical analysis of the asphalt mixtures shows that six mixes have promising responses in terms of stiffness, tensile resistance, and water susceptibility. Nevertheless, the high variability of recycled materials and by-products has to be taken into consideration during the definition of alternative binders and recycled asphalt mixtures. In fact, this study highlights the crucial effects of the chemical composition of the constituents and their compatibility on the behaviour of the final product. This preliminary study represents a first attempt to define alternative binders, which can be used in combination with recycled aggregates for producing more sustainable road materials. However, further analysis is necessary in order to assess the durability and the ageing tendency of the materials.     

Alternative Extraction and Downstream Purification Processes for Anthocyanins

Anthocyanins are natural pigments displaying different attractive colors ranging from red, violet, to blue. These pigments present health benefits that increased their use in food, nutraceuticals, and the cosmetic industry. However, anthocyanins are mainly extracted through conventional methods that are time-consuming and involve the use of organic solvents. Moreover, the chemical diversity of the obtained complex extracts make the downstream purification step challenging. Therefore, the growing demand of these high-value pigments has stimulated the interest in designing new, safe, cost-effective, and tunable strategies for their extraction and purification. The current review focuses on the potential application of compressed fluid-based (such as subcritical and supercritical fluid extraction and pressurized liquid extraction) and deep eutectic solvents-based extraction methods for the recovery of anthocyanins. In addition, an updated review of the application of counter-current chromatography for anthocyanins purification is provided as a faster and cost-effective alternative to preparative-scale HPLC.     

Chemical Composition and Metabolomic Analysis of Amaranthus cruentus Grains Harvested at Different Stages

This study aimed at investigating the impact of early versus normal grain harvesting on the chemical composition and secondary metabolites of Amaranthus cruentus species grown in South Africa. Mature harvested grain had higher (p < 0.05) DM, CF, NDF and ADF content compared to prematurely harvested grain. There were no significant (p > 0.05) differences between CP, ADL and GE of premature and mature harvested grains. Mature harvesting resulted in higher grain Ca, P, Mg and K content. Essential amino acids spectrum and content remained similar regardless of maturity at harvest. The grains displayed an ample amount of unsaturated fatty acids; the highest percentage was linoleic acid: 38.75% and 39.74% in premature and mature grains, respectively. β-Tocotrienol was detected at 5.92 and 9.67 mg/kg in premature and mature grains, respectively. The lowest was δ-tocotrienol which was 0.01 and 0.54 mg/kg in premature and mature grains, respectively. Mature harvested grain had a higher secondary metabolite content compared to premature harvested grains. The results suggest that mature harvested Amaranthus cruentus grain contain more minerals and phytochemicals that have health benefits for human and livestock immunity and gut function, which ultimately improves performance. This study concludes that A. cruentus grown in South Africa is a potential alternative cereal to major conventional cereals.     

Fluorine Substitution of TCNQ Alters the Redox-Driven Catalytic Pathway for the Ferricyanide-Thiosulfate Reaction

Mechanistic variation in catalysis through substituent-based redox tuning is well established. Fluorination of TCNQ (TCNQ=tetracyanoquinodimethane) provides ~850 mV variation in the redox potentials of the and (n=0, 2, 4) processes. With , catalysis of the kinetically very slow ferrocyanide-thiosulfate redox reaction in aqueous solution occurs via a mechanism in which the catalyst is reduced to when reacting with which is oxidised to . Subsequently, reacts with to form and reform the catalyst, in another thermodynamically favoured process. An analogous mechanism applies with as a catalyst. In contrast, since the reaction of with is thermodynamically unfavourable, an alternative mechanism is required to explain the catalytic activity observed in this non-fluorinated system. Here, upon addition of , reduction of to occurs with concomitant oxidation of to , which then acts as the catalyst for oxidation. Thermodynamic data explain the observed differences in the catalytic mechanisms. (n=0, 4) also act as catalysts for the ferricyanide-thiosulfate reaction in aqueous solution. The present study shows that homogeneous pathways are available following addition of these dissolved materials. Previously, these (n=0, 4) coordination polymers have been regarded as insoluble in water and proposed as heterogeneous catalysts for the ferricyanide-thiosulfate reaction. Details and mechanistic differences were established using UV-visible spectrophotometry and cyclic voltammetry.