On Constructive number fields and computability of solutions of PDEs

In this paper we find a connection between constructive number fields and computable reals. This connection is applied to prove the computability in the rigorous sense of computable analysis) of solutions of some important systems of partial differential equations, by means of algorithms which are really used in numerical analysis.     

Asymptotic integration of the Riccati equation by methods of power geometry

The Riccati equation is considered. Both continuable and noncontinuable solutions of this equation are studied. Asymptotic representations of its solutions are obtained by power geometry methods.     

Exit Times,Overshoot and Undershoot for a Surplus Process in the Presence of an Upper Barrier

We study the movement of a surplus process with initial capital u in the presence of two barriers: a lower barrier at zero and an upper barrier at b (b > u). More specifically, we consider the behaviour of the surplus: (a) in continuous time; and (b) only at claim arrival times. For each of these cases, we find the expected time until the process exits the interval [0,b]. We also obtain results related to the undershoot and overshoot of the surplus which, in particular for case (b) above, are derived under the assumption that the distribution of claim sizes and/or claim interarrival times belongs to the mixed Erlang class. In the final section we discuss the implementation of the methods in a number of examples using computer algebra software. These examples illustrate the efficiency of the methods even in fairly complicated cases.     

Roots of Unity in Orders

We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in the group of roots of unity can be solved in polynomial time. As an auxiliary result, we solve the discrete logarithm problem for certain unit groups in finite rings. Our techniques, which are taken from commutative algebra, may have further potential in the context of cryptology and computer algebra.     

A family of models with blue sky catastrophes of different classes

A generalized model with bifurcations associated with blue sky catastrophes is introduced. Depending on an integer index m, different kinds of attractors arise, including those associated with quasi-periodic oscillations and with hyperbolic chaos. Verification of the hyperbolicity is provided based on statistical analysis of intersection angles of stable and unstable manifolds.     

Janis Stradins: An outstanding electrochemist and expert in the history of science

Journal of Solid State Electrochemistry - Janis Stradins (10.12.1933 – 29.11.2019) was a well-known expert in molecular electrochemistry, ESR spectroscopy and physical organic chemistry, as...     

Interspecific Variation between the American Quercus virginiana and Mediterranean Quercus Species in Terms of Seed Nutritional Composition,Phytochemical Content,and Antioxidant Activity

This study aimed to evaluate a complete nutritional composition in the seeds Quercus virginiana to compare this nutritional composition with three Mediterranean Quercus species. We analyzed the seed morphometry, proximate composition, phytochemicals, and antioxidant capacity. The seed of Q. virginiana presented the smaller seed size and weight, while Q. suber presented the highest values. Moreover, Q. virginiana seeds showed the highest amounts of sugar and total lipids, digestibility, energy, palmitic acid, and stearic acid. On the other hand, Q. virginiana seeds showed the lowest values of linoleic acid. Moreover, Q. coccifera seeds presented the highest total phenolics and flavonoids contents and antioxidant activity. The clustering analysis revealed a significant similarity in seed morphometry and nutritional composition between the Mediterranean Q. ilex and Q. suber, grouping with the American Q. virginiana, but to a considerable distance; by contrast, the Mediterranean Q. coccifera was the most distant in the clustering analysis. The content of phenolics and flavonoids and digestibility value were the variables that contributed to the separation to a greater extent in the clustering of the four species. The nutritional and biological activity assessment of plant seed may be considered as an essential mission to find new sustainable sources and novel chemical agents. In this sense, Quercus seeds may be an alternative and a competitive food source for the agri-food industry.     

One-Pot and Two-Chamber Methodologies for Using Acetylene Surrogates in the Synthesis of Pyridazines and Their D-Labeled Derivatives

Acetylene surrogates are efficient tools in modern organic chemistry with largely unexplored potential in the construction of heterocyclic cores. Two novel synthetic paths to 3,6-disubstituted pyridazines were proposed using readily available acetylene surrogates through flexible C₂ unit installation procedures in a common reaction space mode (one-pot) and distributed reaction space mode (two-chamber): (1) an interaction of 1,2,4,5-tetrazine and its acceptor-functionalized derivatives with a CaC₂−H₂O mixture performed in a two-chamber reactor led to the corresponding pyridazines in quantitative yields; (2) [4+2] cycloaddition of 1,2,4,5-tetrazines to benzyl vinyl ether can be considered a universal synthetic path to a wide range of pyridazines. Replacing water with D₂O and vinyl ether with its trideuterated analog in the developed procedures, a range of 4,5-dideuteropyridazines of 95–99% deuteration degree was synthesized for the first time. Quantum chemical modeling allowed to quantify the substituent effect in both synthetic pathways.     

Silver as a capturing material for iodine released from lead–bismuth eutectic in various conditions

Journal of Radioanalytical and Nuclear Chemistry - The usage of silver as a filtering material for removal of iodine from the gas phase of a lead–bismuth eutectic based nuclear reactor was...