On sequential traversal of sets

The problem of sequential traversal of megapolises with precedence conditions is investigated; this problem is oriented to mechanical engineering — CNC metal cutting machines. There is the following setting singularity: the terminal component of additive criterion contains the dependence on the starting point. This singularity leads to the fact that the natural solution procedure based on dynamic programming must be applied individually for every starting point. The investigation goal consists in the construction of an optimizing algorithm for determining a complex including a route (a variant of megapolis numbering), a trajectory, and a starting point. The proposed algorithm realizes an idea of directed enumeration of starting points. This algorithm is realized as a program for PC; computations for model examples are made.

ON ROUTING PROBLEM WITH STARTING POINT OPTIMIZATION

One problem focused on engineering applications is considered. It is assumed that sequential visits to megacities have been implemented. After all visits have been made, it is required to return to the starting point (a more complex dependence on the starting point is also considered). But the last requirement is not strict: some weakening of the return condition is acceptable. Under these assumptions, it is required to optimize the choice of starting point, route, and specific trajectory. The well-known dynamic programming (DP) is used for the solution. But when using DP, significant difficulties arise associated with the dependence of the terminal component of the criterion on the starting point. Starting point enumeration is required. We consider the possibility of reducing the enumeration associated with applied variants of universal (relative to the starting point) dynamic programming. Of course, this approach requires some transformation of the problem.

To the question of optimization of the starting point in the routing problem with restrictions

We consider the extreme routing problem with an additive criterion, the terminal component of which depends on the starting point. This dependence may be associated, in particular, with the requirement to return to the starting point region after completing the final system of tasks that need to be ordered. The work assumes that the tasks to be performed are related with visiting non-empty finite sets called megacities. In turn, the mentioned visits are associated with the performance of works, the costs of which are involved in the formation of the criterion. Finally, the costs of external movements (between megacities) supplement the formation of an additive criterion to be minimized. It is required to find a global extremum and a solution that includes a starting point, the order of visits to megacities and a specific trajectory of the process. The solution uses widely understood dynamic programming (DP). It is significant that procedures based on DP use starting point. Therefore, enumeration of mentioned points is required. The article proposes an approach to solving the problem of reducing this enumeration through the use of auxiliary DP that are universal with respect to the choice of a starting point. The optimal algorithm was built and implemented on a PC using the aforementioned approach.

Isolation, absolute configuration and bioactivities of megastigmanes or C13 isonorterpinoides

Megastigmanes or C13 isonorterpenoids a terpene class of compounds, specially the title compounds are related to sesquiterpenoides but due to C13 skeleton also it is called as norterpenoides. Most of the megastimane compounds have been isolated from the plant source such as Cucumis sativus, Crotalaria zanzibarica, staphylea bumalda, Juniperus communis and Excoecaria cohinchinensis etc. Few reports were showing the megastimane compounds are showing potencial activity against scavenging radical (DPPH) and hepatoprotective activities. The classification of C13 norisoprenoides, are assumed to be apocarotenoides that is formed from the degradation of carotenoides by the action of carotenoides cleavage dioxygenases which have been isolated from various plants. The majority of the evidences for this assumption is the similarly between most megastigmanes and the terminal component of plant carotenoides. Because such compounds are generally not oxygenated at C7 but commonly oxygenated at C9 presumably as a result of the oxidative cleavage of the acyclic portion of caritenoides, the key step in megastigmanes formation has been thought to be transportion of oxygen from C9 to C7. Hence, based on the above information the C9 position and its absolute configuration is very important to get potential activity against various diseases, in this progression a lot of literature reports were showing the importance and absolute configuration at C9 position in megastigmanes or C13 norisoprenoides. In this review, we are reporting the chemistry, absolute configuration and bioactivities of megastigmanes or C13 norisoterpenoides. To our knowledge, this is the first review on megastimanes and its absolute configuration.