Publish in OALib Journal
APC: Only $99
In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logarithmic and identric means using nothing more than basic calculus. Of course, these results are all well-known and several proofs of them and their generalizations have been given. See [1-6] for more information. Our goal here is to present a unified approach and give the proofs as corollaries of one basic theorem.
In the present paper, we answer the question: for 0 < α < 1 fixed, what are the greatest value p(a) and the least
value q(a) such that the inequality.
For more information about abstract,please download the PDF file.
In this paper, we have suggested a new technique to transform multi-objective linear programming problem (MOLPP) to the single objective linear programming problem by using Harmonic mean for values of function and an algorithm is suggested for its solution, the computer application of algorithm has been demonstrated by solving some numerical examples. We have used some other techniques, such as (sen, arithmetic mean, median) to solve the same problems, the results in Table 3 indicate that the new technique in general is promising.
This paper presents the impact of mean maximum temperature on Chitral river basin situated at Chitral district and high altitude (>6000 m) peaks of the Hindukush range under changing climate in Pakistan. The analysis of Chitral River as one of the tributary of Kabul River—the second largest river of Pakistan—revealed that change in temperature has a profound influence on the snow/glacial melt in comparison to the mean monthly rainfall. This is because the studied river is faded by the snow and glacial melt and receives a lot of snowfall from winter (DecFeb) to pre-monsoon (April-May). In monsoon period (Jul-Sep), 30% of the time the discharge rate remains above the mean while 60% of the time the discharge is less than the mean in the pre-monsoon (April-May) period. It means that 10% of the time the discharge is in reach of 300% to 900% of the mean flow, showing a rise in water yield and river discharge rate due to increase in mean monthly maximum temperature. Due to this significant increase (p < 0.05), the glaciers start melting faster and disappear in early summer, hence, reducing their residency period to convert into ice. This shows the signals of changing climate transfer into hydrological changes in Pakistan. Our findings are important for agriculture, hydropower and water management sectors for future planning especially in dry season for sustainable food security and for operation of ydrological installations in the country.
In the present paper, we answer the question: for 0< a <1 fixed, what are the greatest value p(a)
and the least value q(a) such that the double inequality Jp(a,b)< aA(a,b)+ (1-a)G(a,b)<Jq(a,b)
holds for all a,b>0 with a is not equal to b ?
It refers to the sum total of value system, behavioral norms and social relationships accepted by young generations for youth culture which has the characteristic of hierarchy, variability and rebellion. It has also had positive and negative functions. It is the mutual influence and mutual promoting relationship between the youth culture and advanced culture. Comrade Hu Jintao puts forward three wishes to the majority of young people, but also gives the youth culture three new elements, which are diligent in learning, good at creating and making contribution. In the new period, the youth culture will further be boosted when we are developing advanced culture.