Given a graph G, a graph F is said to be RAMSEY for G if in every edge coloring of F with two colors, there exists a monochromatic copy of G. The minimum NUMBER of edges of a graph F which is RAMSEY for G is called the size-RAMSEY NUMBER of G and is denoted by ^r(G). In 1983, Beck gave a linear upper bound (in terms of n) for ^r(Pn), where Pn is a path on n vertices, giving a positive answer to a question of Erd}os. After that, different approaches were attempted by several authors to reduce the upper bound for ^r(Pn) for sufficiently large n and most of these approaches are based on the classic models of random graphs. Also, Haxell and Kohayakama in 1994 proved that the size RAMSEY NUMBER of the cycle Cn is linear in terms n, however the Szemeredi's regularity lemma is used in their proof and so no speci c constant coefficient is provided. Here, we provide a method to obtain an upper bound for the size RAMSEY NUMBER of a graph using good expander graphs such as Ramanujan graphs. In particular, we give an alternative proof for the linearity of the size RAMSEY NUMBER of paths and cycles. Our method has two privileges in compare to the previous ones. Firstly, it proves the upper bound for every positive integer n in comparison to the random graph methods which needs n to be sufficiently large. Also, due to the recent explicit constructions for bipartite Ramanujan graphs by Marcus, Spielman and Srivastava, we can constructively  nd the graphs with small sizes which are RAMSEY for a given graph. We also obtain some results about the bipartite RAMSEY NUMBERs.

In 1991, McKay and Radziszowski proved that, however each 3-subset of a 13-set is assigned one of two colours, there is some 4-subset whose four 3-subsets have the same colour. More than 25 years later, this remains the only non-trivial classical RAMSEY NUMBER known for hypergraphs. In this article, we nd all the extremal colourings of the 3-subsets of a 12-set and list some of their properties. We also provide an answer to a question of Dudek, La Fleur, Mubayi and Rodl about the size-RAMSEY NUMBERs of hypergraphs.

For two given graphsG1 and G2, the RAMSEY NUMBER R (G1, G2) is the smallest integer n such that for any graph G of order n, either Gcontains G1 or the complement of G contains G 2. Let Tn denote a tree of order n and Wm a wheel of order m+1. To the best of our knowledge, only R (Tn, Wm) with small wheels are known. In this paper, we show thatR (Tn, Wm) =3n-2 for odd m with n>756 m10.

According to textbook arguments marginal cost pricing scores first on the effciency ground. However,if the monopolistic firm benefits from increasing returns to scale, the industry will not be financially viable. If this is the case, one option, which maximizes the welfare subject to a break-even constraint, is RAMSEY Pricing. In this study this method of pricing is applied to the Iranian Electricity Industry.The prices are offered for different types of usage (residential, agricultural, public and commercial). The present study applies the direct price elasticity of demand for each usage as well as the marginal cost of producing, transmitting and distributing electricity.These prices are cpmputed by using a programme in MATLAB environment for peak and off-peak periods. Finally, the resulting welfare changes arising from applying RAMSEY Pricing as an alternative model are estimated, and proven to be positive on balance.

The serious obstacles to improve water supply, has caused world debates, seeking some solutions to tackle the problem of shortages in water supply. t. Therefore, programs and policies have focused mainly on appropriate pricing approach of. Since the water industry in Iran has been monopolized by the government, an effective pricing approach is assumed to maximize the social welfare with consideration to the cost.. To consider the mentioned aspects to price water, this study used the RAMSEY approach. Thy study estimated the RAMSEY price of water used for the agricultural sector in Hamadan province of Iran. To determine the price, the Agricultural water demand function was estimated using time series data for the years 1370-88. Using the estimated demand function the price elasticity of demand was calculated. The water production function was also estimated using time series data for the years 1370-88. In order to estimate supply and demand functions, the ARDL model and Microfit econometric software were used. Using production function and demand function, the marginal cost and price elasticity were calculated. Applying the calculated ratios through MATLAB software, the RAMSEY price of water for agriculture was measured. According to the results of this study, in the year 1388 the RAMSEY price of water for agriculture was more than the paid price for industry.

The aim of this study is to investigate optimal monetary and fiscal policies for the Iranian economy considering RAMSEY problem. Using a Dynamic Stochastic General Equilibrium model, the effects of imposing various taxes such as consumption tax, capital income tax, labor income tax and profit tax are examined by different scenarios. The results indicate that Friedman’ s rule, or zero inflation is determined as optimal monetary policy under scenarios with and without price rigidities. In addition, since the governments try to minimize the distortions from taxes levied on different economic sectors, necessity of a subsidy or negative tax is confirmed under RAMSEY conditions. According to the findings, the inflation rate not only depends on nominal and real rigidities assumed in the model, but also to the NUMBER of instruments available to the RAMSEY planner.

Introduction: One of the causes of error and perturbation in isodose curves in conventional radiotherapy treatment planning is the existence of tissues having either very high density (bone, prosthesis) or very low density (lung, air cavities). Nowadays, the use of CT images to solve this problem is growing, and so is the need for calibration curves that convert the CT-NUMBER of the tissue to electron density for dose calculation. The conventional method to obtain this curve is purely measurement-based, in which a phantom containing various materials of known electron densities is imaged. Alternatively, a more fundamental method of stoichiometry has been used in this work.Material and Methods: For the stoichiometric method, initially a cylindrical polyethylene phantom was built. The phantom consists of inserts of high-purity aluminum, PVC, polyethylene, water and cork to model hard bone, skeleton, fat, muscle and lung tissues, respectively. CT imaging was then performed at 120 kVp using a spiral CT scanner (GE model NXI). A system of simultaneous equations was solved to get the appropriate CT-NUMBER to electron-density conversion for each tissue type using the CT-NUMBERs from the phantom images, the physical and radiological data of the materials. A conversion curve showing the variation of CT-NUMBER with relative electron density was also plotted. The result of the stoichiometric conversion was then compared to that from other methods.Results: The system of simultaneous equations yielded the factors, the experimental and the computed CT-NUMBERs were compared. The highest uncertainty was estimated to be approximately 5.6% for a relatively high-density material such as aluminum and 4% for polyethylene. The curves representing the electron density based on CT-NUMBER start diverging at CT-NUMBER equal to zero and above.Discussion and Conclusion: Comparing the results obtained from the experimental and computational methods suggest an acceptable level of accuracy for the computational (stoichiometric) conversion. The uncertainty in the electron density obtained is greater for materials of higher electron density.

Water is a necessary and scarce good that requires new strategies for allocation and optimal use. we. Water pricing and levying suitable tariffs subject to social welfare maximization are the economic solution to this problem. In this study, we have considered available tariffs in domestic water sector of the city of Neyshabour. According to current tariff problems, new tariffs are offered by using RAMSEY Model with the target of maximization of social welfare. Finally, RAMSEY tariffs are modified based on two scenarios. In the first one, we incur less cost to customers with paying a subsidy about 135.5 Rial/m3/year by government. In this scenario, the minimum cost is zero for users with consumption less than 5 m3/month and the maximum cost is 1216 Rial/m3/month for users with consumption more than 30 m3/month. In the second one, losses related to low income group’s paying are compensated by high income users. So, minimum cost is zero for users with consumption less then 5 m3/month, and maximum cost is 1980 Rial/m3/month for users with consumption more than 40 m3/month. In these two scenarios, the water and wastewater company would be in the break even point.

Public pricing of products is one of the most important economical issues, since any changes in the pricing, affects both the welfare of consumers and quantity of goods and Services which are produced. This paper deals with the optimal gas pricing in different sectors, including households, public- commercial and industrial sectors by the RAMSEY method of pricing. In this regard, at the first market demand is estimated and then price elasticitiy’s of demand for different sectors of economy are calculated. Regarding to Ramsay pricing method which, is based on the assumption of increasing return to scale, and one of its application is natural monopoly, after the estimation of natural gas production function, the issue of existence of increasing return to scale is surveyed in this industry. After determination of production function, marginal cost of industry is calculated. And at the end with solving RAMSEY equation system via Matlab software, optimal prices in all sectors are calculated in 2006, and compared with the current prices. These prices are estimated on the basis of demand elasticities in different sectors and non- lose of Khorasan Gas Company.

Because of water resources scarcity and increasing demand due to population growth, water resources management plays a key role in keeping the balance between supply and demand. Economic tools such as pricing are greatly contributing in this regard. The aim of this study was to determine the optimal price of water for domestic uses in the city of Tehran. For this purpose, the Demand functions were estimated using regression analysis for different consumption levels. Water production cost was derived using Translog cost function. Suitable price was suggested based on the price elasticity of water demand and marginal cost of production, in the framework of RAMSEY model for each consumption level. Data of water consumption for period of 1975-2014 in the city of Tehran was used. The results showed that the price elasticity of water demand includes the range of -0.03 to -0.42, in such a way that for higher consumption levels the price elasticity of demand increases, showing higher share of water cost in the household budget. The production final cost for one cubic meter of water is calculated as 6719 Rials. Average optimal price computed by RAMSEY method was variable for different levels and price elasticity of water consumption was dependent on each level. The results indicated that the RAMSEY optimal water price for using one cubic meter of water was 2209 Rials for the lowest level and 25373 Rials for the highest level. Our results suggested that, in all the levels of the water use, RAMSEY price is higher than the price paid by the consumers. Therefore it is recommended to increase the price for all levels of domestic water consumption in an stepwise pattern so that it would get closer to the RAMSEY Prices.