The critical behavior of the Ginzburg-Landau model is described in a manifestly gauge-invariant manner. The gauge-invariant correlation-function exponent is computed to first order in the 4-d and 1/n expansion, and found to agree with the ordinary exponent obtained in the covariant gauge, with the parameter alpha=1-d in the gauge-fixing term ( partial differential (mu)A(mu))(2)/2alpha.

This article concerns the existence of positive solutions for thesecond order equation involving a nonlocal term $$ -\Delta u=\gamma (-\Delta)^{-1} u+|u|^{p-1}u, under Dirichlet boundary conditions. We prove depending on real parameter \(\gamma>0\), and up to critical value exponent \(p\), i.e. when \(1<p\leq 2^*-1\), where \(2^*=\frac{2N}{N-2}\) is Sobolev exponent. For \(p=2^*-1\), this...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

Based on continued fractions Wiener showed that a typical RSA system can be totally broken if its secret exponent d < 25 . 0 N where N is the RSA modulus. Recently, based on lattice basis reduction, Boneh and Durfee presented a new short secret exponent attack which improves Wiener’s bound up to d < 292 . 0 N . In this paper we show that it is possible to use a short secret exponent which is lo...

Let n = pq be an RSA modulus with unknown prime factors of equal bit-size. Let e be the public exponent and d be the secret exponent satisfying ed ≡ 1 (mod φ(n)) where φ(n) is the Euler totient function. To reduce the decryption time or the signature generation time, one might be tempted to use a small private exponent d. Unfortunately, in 1990, Wiener showed that private exponents smaller than...

The effects of uncertainties in the gas-surface interaction and intermolecular interaction models on the hypersonic boundary layer development are investigated using the non-intrusive generalized polynomial chaos method. In particular, uncertainties in the surface shear stress, normal stress, heat flux, flowfield temperature and density resulting from uncertain viscosity exponent, surface tempe...

We analyze the partition function of the dimer model on an M×N triangular lattice wrapped on a torus obtained by Fendley, Moessner, and Sondhi [Phys. Rev. B 66, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by a conformal field theory having a central charge c=-2. The shift exponent for the specific heat is found to depend on t...

Dynamics and morphology of hole growth in a film of power hardening viscoplastic solid [ yield stress approximately (strain-rate)(n)] is investigated. At short times the growth is exponential and depends on the initial hole size. At long times, for n>1 / 3, the growth is again exponential but with a different exponent. However, for n<1 / 3 the hole growth slows and the hole radius approaches an...

In 1995, Kuwakado, Koyama and Tsuruoka presented a new RSA-type scheme based on singular cubic curves y2 ≡ x3+bx2 (mod N) where N = pq is an RSA modulus. Then, in 2002, Elkamchouchi, Elshenawy and Shaban introduced an extension of the RSA scheme to the field of Gaussian integers using a modulus N = PQ where P and Q are Gaussian primes such that p = |P| and q = |Q| are ordinary primes. Later, in...

We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents gamma including random networks. For gamma>3 , the critical fitness value f(c) approaches a nonzero finite value in the limit N --> infinity, whereas f(c) approaches zero as 2(N) on the networks ...