Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

Chemical diversity and potential biological functions of the pygidial gland secretions in two species of Neotropical dung roller beetles

Dung roller beetles of the genus Canthon (Coleoptera: Scarabaeinae) emit an odorous secretion from a pair of pygidial glands. To investigate the chemical composition of these secretions, we used stir bar sorptive extraction (SBSE), coupled with gas chromatography–mass spectrometry (GC–MS) for analysis of extracts of pygidial gland secretions secreted by the dung roller beetles Canthon femoralis femoralis and Canthon cyanellus cyanellus. Chemical analyses of volatiles collected from pygidial gland secretions comprise a great diversity of the functional groups. Chemical profile comparisons showed high intra- and interspecific variability. The pygidial gland secretion of Canthon f. femoralis was dominated by sesquiterpene hydrocarbons, whereas the profile of Canthon c. cyanellus was dominated by carboxylic acids. The different pygidial secretions have a high diversity of chemical compounds suggesting a multifunctional nature involving some key functions in the biology. We discuss the biological potential of these compounds found in the pygidial glands of each species with respect to their ecological and behavioral relevance.

On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ Fn2 | w( f ⊕la) = 2n−1+2 n 2 −1} and {a ∈ Fn2 | w( f ⊕la) = 2n−1−2 n 2 −1} respectively, where w( f ⊕ la) denotes the Hamming weight of the Boolean function f (x) ⊕ la(x) and la(x) is the linear function defined by a ∈ Fn2 . f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) ⊕ f1(x) ⊕ f2(x) ⊕ f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.