Proving a constructive version of the Spectral Mapping Theorem, Bridges and Havea used a constructive semigroup with inequality in . This motivated us to achieve a little progress in that direction. The starting point is the structure (S,=,≠,·) called a semigroup with apartness. Our primary objective is to prove isomorphism theorems for such constructive semigroups. In doing so our main ideas and notions come from .
We examine basic notions of special subsets and orders in the context of semigroups with apartness and prove constructive analogues of some classical theorems relating such subsets and orders.
Modern tendencies in the development of diesel engines include the operation of the system for injecting diesel fuel at pressures higher than 100 MPa. Knowing the characteristics of liquid fuels such as speed of sound, bulk modulus and density depending on pressure, is important for predicting the behavior of fuel injection systems for diesel engines and optimization of the same. The paper presents an original method and apparatus (device) for determining the speed of sound and density of fluids depending on the pressures. With this method, values of these characteristics for rapeseed oil, biodiesel and conventional diesel fuel at pressures up to 160 MPa are determined. The method is non-destructive, it can also be applied to higher pressures than 160 MPa, as well as other liquid fluids that are used at high pressure - hydraulic oil, for example
A semiring variety is d-semisimple if it is generated by the distributive
lattice of order two and a finite number of finite fields. A d-semisimple
variety V = HSP{B2, F1,..., Fk} plays the main role in this paper. It will be
proved that it is finitely based, and that, up to isomorphism, the
two-element distributive lattice B2 and all subfields of F1,..., Fk are the
only subdirectly irreducible members in it. [The first author is supported by
China Postdoctoral Science Foundation, Grant 2011M501466 and the Natural
Science Foundation of Shannxi Province, Grant 2011JQ1017. The second authoris
Supported by the Ministry of Education, Science and Technological Development
of Serbia,Grant 174018. The third author is Supported by the Ministry of
Education, Science and TechnologicalDevelopment of Serbia, Grant 174026]
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