scholarly journals Finding Domatic Partitions in Infinite Graphs

10.37236/5089 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Matthew Jura ◽  
Oscar Levin ◽  
Tyler Markkanen
Keyword(s):  
Computability Theory ◽  
Infinite Graphs ◽  
Optimal Size ◽  
Regular Graphs ◽  
Domatic Number

We investigate the apparent difficulty of finding domatic partitions in graphs using tools from computability theory.  We consider nicely presented (i.e., computable) infinite graphs and show that even if the domatic number is known, there might not be any algorithm for producing a domatic partition of optimal size.  However, we prove that smaller domatic partitions can be constructed if we restrict to regular graphs.  Additionally, we establish similar results for total domatic partitions.

scholarly journals The signed domatic number of some regular graphs

2009 ◽  
Vol 157 (8) ◽  
pp. 1905-1912 ◽  
Author(s):  
Dirk Meierling ◽  
Lutz Volkmann ◽  
Stephan Zitzen
Keyword(s):  
Regular Graphs ◽  
Domatic Number

The Experience of Industrialization under NEPand Its Application in the Current Conditions

2013 ◽  
pp. 109-135
Author(s):  
Y. Goland
Keyword(s):  
Economic Policy ◽  
Capital Formation ◽  
Optimal Size ◽  
Popular Belief ◽  
New Economic Policy ◽  
Relevant Today ◽  
Domestic Capital

The article refutes popular belief about the necessity to abolish the New Economic Policy (NEP) of the 1920s for the purpose of industrialization. It is shown that it started successfully under NEP although due to a number of reasons the efficiency of the investments was low. The abolishment of NEP was caused not by the necessity to accelerate the industrialization but by the wrong policy towards the agriculture that stopped the development of farms. The article analyzes the discussion about possible rates of the domestic capital formation. In the course of this discussion, the sensible approach to finding the optimal size of investments depending on their efficiency was offered. This approach is still relevant today.

Determination of Optimal Reserve between Two Machines in Series with the Repair Time has Change of Distribution after the Truncation Point

GIS Business ◽  
2019 ◽  
Vol 14 (6) ◽  
pp. 577-585
Author(s):  
T. Vivekanandan ◽  
S. Sachithanantham
Keyword(s):  
Real Life ◽  
Random Variable ◽  
Repair Time ◽  
Inventory Level ◽  
Optimal Size ◽  
Truncation Point ◽  
In Series ◽  
Optimal Reserve ◽  
Optimal Inventory Level ◽  
Two Machines

In inventory control, suitable models for various real life systems are constructed with the objective of determining the optimal inventory level.  A new type of inventory model using the so-called change of distribution property is analyzed in this paper. There are two machines M1 and M2  in series and the output of M1 is the input of M2. Hence a reserve inventory between M1 and M2 is to be maintained. The method of obtaining the optimal size of reserve inventory, assuming cost of excess inventory, cost of shortage and when the rate of consumption of M2  is a constant, has already been attempted.  In this paper, it is assumed that the repair time of M1  is a random variable and the distribution of the same undergoes a change of distribution  after the truncation point X0 , which is taken to be a random variable.  The optimal size of the reserve inventory is obtained under the above said  assumption . Numerical illustrations are also provided.

Study of the Composite Materials Optimal Structure Containing a Hollow Aluminum and Silica Microsphere Dependence on Humidity

2020 ◽  
Vol 12 ◽  
Author(s):  
Alexandra Atyaksheva ◽  
Yermek Sarsikeyev ◽  
Anastasia Atyaksheva ◽  
Olga Galtseva ◽  
Alexander Rogachev
Keyword(s):  
Composite Material ◽  
Composite Materials ◽  
Strength Function ◽  
Theory And Practice ◽  
Optimal Structure ◽  
Optimal Size ◽  
Structure And Properties ◽  
Power Functions ◽  
Silica Microsphere ◽  
Heat Engineering

Aims:: The main goals of this research are exploration of energy-efficient building materials when replacing natural materials with industrial waste and development of the theory and practice of obtaining light and ultra-light gravel materials based on mineral binders and waste dump ash and slag mixtures of hydraulic removal. Background.: Experimental data on the conditions of formation of gravel materials containing hollow aluminum and silica microsphere with opportunity of receipt of optimum structure and properties depending on humidity with the using of various binders are presented in this article. This article dwells on the scientific study of opportunity physical-mechanical properties of composite materials optimization are considered. Objective.: Composite material contains hollow aluminum and silica microsphere. Method.: The study is based on the application of the method of separation of power and heat engineering functions. The method is based on the use of the factor structure optimality, which takes into account the primary and secondary stress fields of the structural gravel material. This indicates the possibility of obtaining gravel material with the most uniform distribution of nano - and microparticles in the gravel material and the formation of stable matrices with minimization of stress concentrations. Experiments show that the thickness of the cement shell, which performs power functions, is directly related to the size of the raw granules. At the same time, the thickness of the cement crust, regardless of the type of binder, with increasing moisture content has a higher rate of formation for granules of larger diameter. Results.: The conditions for the formation of gravel composite materials containing a hollow aluminosilicate microsphere are studied. The optimal structure and properties of the gravel composite material were obtained. The dependence of the strength function on humidity and the type of binder has been investigated. The optimal size and shape of binary form of gravel material containing a hollow aluminosilicate microsphere with a minimum thickness of a cement shell and a maximum strength function was obtained. Conclusion.: Received structure allows to separate power and heat engineering functions in material and to minimize the content of the excited environment centers.

Sign in / Sign up

Export Citation Format

Share Document