6,630 research outputs found
Quark-Lepton Quartification
We propose that quarks and leptons are interchangeable entities in the
high-energy limit. This naturally results in the extension of [SU(3)]^3
trinification to [SU(3)]^4 quartification. In addition to the unbroken color
SU(3)_q of quarks, there is now also a color SU(3)_l of leptons which reduces
to an unbroken SU(2)_l. We discuss the natural occurrence of SU(2)_l doublets
at the TeV energy scale, which leads remarkably to the unification of all gauge
couplings without supersymmetry. Proton decay occurs through the exchange of
scalar bosons, with a lifetime in the range 10^{34} - 10^{36} years.Comment: 12 pages, 4 figures. Reference adde
Goodness-of-fit tests when parameters are estimated
Several nonparametric goodness-of-fit tests are based on the empirical distribution function. In the presence of nuisance parameters, the tests are generally constructed by first estimating these nuisance parameters. In such a case, it is well known that critical values shift, and the asymptotic null distribution of the test statistic may depend in a complex way on the unknown parameters. In this paper we use bootstrap methods to estimate the null distribution. We shall consider both parametric and nonparametric bootstrap methods. We shall first demonstrate that, under very general conditions, the process obtained by subtracting the population distribution function with estimated parameters from the empirical distribution has the same weak limit as the corresponding bootstrap version. Of course in the nonparametric bootstrap case a bias correction is needed. This result is used to show that the bootstrap method consistently estimates the null distributions of various goodness-of-fit tests. These results hold not only in the univariate case but also in the multivariate setting
A CRITICAL STUDY ON THE CONCEPT OF WELFARE STATE AND WELFARE SCHEMES
The welfare state takes the accountability of security, protection and support of the economic and social well-being of its people. The government gives attention to such people of the state who are not capable of avail themselves of the minimum necessities of a good life. These are mainly like food, cloth, shelter, pension, health insurance etc. It is the moral duty of a welfare state to provide such facilities to the needy sections of the society. The welfare of its citizens remains on the main concern list of the state. Previously, India was not a welfare state because of the foreigner’s autocratic rule. India was not a welfare state under the British rule. They have no equal rights. Even their life is not safe under their rule. Whatever developments British did was in keeping with the benefits of the British colonial government. The industrialization and taxes levied by British government damaged the agro-artisan based economy. It caused poverty in India. Their policies were not in the interests of the people of India. This paper aims to examine the concept of welfare state and welfare schemes
Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point
summary:Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map with a fixed point and prove that these iterates converge to a fixed point of under certain conditions. This fixed point may be different from . To illustrate this phenomenon, an example is given
The Stability of the Gauge Hierarchy in
It has been shown that the Dimopoulos-Wilczek (or missing-VEV) mechanism for
doublet-triplet splitting can be implemented in models,
which requires no adjoint Higgs fields. This is an advantage from the point of
view of string theory construction. Here the stability of the gauge hierarchy
is examined in detail, and it is shown that it can be guaranteed much more
simply than in . In fact a symmetry ensures the stability of the
DW form of the expectation values to all orders in GUT-scale VEVs. It is also
shown that models based on have the advantages of while permitting complete quark-lepton unification as in
.Comment: 13 pages, LaTe
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