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Search Results: 1 - 10 of 3208 matches for " Gyan Prakash Tripathi "
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Algebraic Elementary Operators on B(E)
Gyan Prakash Tripathi
Tamkang Journal of Mathematics , 2012, DOI: 10.5556/j.tkjm.43.2012.463-468
Abstract: In this paper we have obtained a necessary and sufficient condition for generalized derivations to be algebraic on $B(E)$. Further some results on algebraicness of elementary operators are given.
Antinormal composition operators on $ mbf{ell^2}$
Gyan Prakash Tripathi,Nand Lal
Tamkang Journal of Mathematics , 2008, DOI: 10.5556/j.tkjm.39.2008.347-352
Abstract: A bounded linear operator $ T $ on a Hilbert space $ H $ is called antinormal if the distance of $ T $ from the set of all normal operators is equal to norm of $ T $. In this paper, we give a complete characterization of antinormal composition operators on $ ell^2 $, where $ ell^2 $ is the Hilbert space of all square summable sequences of complex numbers under standard inner product on it.
Nilpotency of Elementary Operators on B(E)
Gyan Prakash Tripathi,Nand Lal
Mathematics , 2012,
Abstract: In this paper, we shall give a necessary and sufficient condition for nilpotency of elementary multiplication operators and some sufficient conditions for elementary operators to be nilpotent on B(E), where E is Banach space.
Bayes Shrinkage Minimax Estimation in Inverse Gaussian Distribution  [PDF]
Gyan Prakash
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.27111
Abstract: In present paper, the properties of the Bayes Shrinkage estimator is studied for the measure of dispersion of an inverse Gaussian model under the Minimax estimation criteria.
Number of sets with small sumset and the clique number of random Cayley graphs
Gyan Prakash
Mathematics , 2007,
Abstract: Let $G$ be a finite abelian group of order $n$. For any subset $B$ of $G$ with $B=-B$, the Cayley graph $G_B$ is a graph on vertex set $G$ in which $ij$ is an edge if and only if $i-j\in B.$ It was shown by Ben Green that when $G$ is a vector space over a finite field $Z/pZ$, then there is a Cayley graph containing neither a complete subgraph nor an independent set of size more than $clog nloglog n,$ where $c$ is an absolute constant. In this article we observe that a modification of his arguments shows that for an arbitrary finite abelian group of order $n$, there is a Cayley graph containing neither a complete subgraph nor an independent set of size more than $c(omega^3(n)log omega(n) +log nloglog n)$, where $c$ is an absolute constant and $omega(n)$ denotes the number of distinct prime divisors of $n$.
A remark on a result of Helfgott, Roton and Naslund
Gyan Prakash
Mathematics , 2014,
Abstract: Let $F(X)= \prod_{i=1}^k(a_iX+b_i)$ be a polynomial with $a_i, b_i$ being integers. Suppose the discriminant of $F$ is non-zero and $F$ is admissible. Given any natural number $N$, let $S(F,N)$ denotes those integers less than or equal to $N$ such that $F(n)$ has no prime factors less than or equal to $N^{1/(4k+1)}.$ Let $L$ be a translation invariant linear equation in $3$ variables. Then any $A\subset S(F, N)$ with $\delta_F(N): = \frac{|A|}{|S(F,N)|} \gg_{\epsilon, F, L}\frac{1}{(\log \log N)^{1-\epsilon}}$ contains a non-trivial solution of $L$ provided $N$ is sufficiently large.
Bulk Viscous Anisotropic Cosmological Models with Generalized Chaplygin Gas with Time Varying Gravitational and Cosmological Constants  [PDF]
Shubha Kotambkar, Gyan Prakash Singh, Rupali Kelkar
Natural Science (NS) , 2015, DOI: 10.4236/ns.2015.76035
Abstract: This paper is devoted to studying the generalized Chaplygin gas models in Bianchi type III space- time geometry with time varying bulk viscosity, cosmological and gravitational constants. We are considering the condition on metric potential \"\". Also to obtain deterministic models we have considered physically reasonable relations like \"\" , and the equation of state for generalized Chaplygin gas given by\"\" . A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behaviour of the models has been discussed.
Sum-free set in finite abelian groups
R. Balasubramanian,Gyan Prakash
Mathematics , 2005,
Abstract: Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. In this paper we shall characterise the largest possible sum-free subsets of G in case the order of G is only divisible by primes which are congruent to 1 modulo 3. The result is based on a recent result of Ben Green and Imre Ruzsa.
Asymptotic formula for sum-free sets in abelian groups
R. Balasubramanian,Gyan Prakash
Mathematics , 2005,
Abstract: Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. Let SF(G) denotes the set of all sum-free subets of $G$ and $\sigma(G)$ denotes the number $ n^{-1}(\log_2 |SF(G)|) $. In this article we shall improve the error term in the asymptotic formula of $\sigma(G)$ which was obtained recently by Ben Green and Ruzsa. The methods used are a slight refinement of methods developed by Ben Green and Ruzsa.
Bulk Viscous Bianchi Type V Space-Time with Generalized Chaplygin Gas and with Dynamical G and Λ  [PDF]
Shubha S. Kotambkar, Gyan Prakash Singh, Rupali R. Kelkar
International Journal of Astronomy and Astrophysics (IJAA) , 2015, DOI: 10.4236/ijaa.2015.53025
Abstract: In this paper, bulk viscous Bianchi type V cosmological model with generalized Chaplygin gas, dynamical gravitational and cosmological constants has been investigated. We are assuming the condition on metric potential \"\". To obtain deterministic model, we have considered physically plausible relations like \"\", and the generalized Chaplygin gas is described by equation of state \"\". A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behavior of the models has been discussed.
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