Fix a prime p > 2. Let ρ : Gal(Q/Q) → GL2(I) be the Galois representation coming from a non-CM irreducible component I of Hida’s p-ordinary Hecke algebra. Assume the residual representation ρ̄ is absolutely irreducible. Under a minor technical condition we identify a subring I0 of I containing Zp[[T ]] such that the image of ρ is large with respect to I0. That is, Im ρ contains ker(SL2(I0) → SL2...

Remark 0.1 (Notation). |G| denotes the order of a finite group G. [E : F ] denotes the degree of a field extension E/F. We write H ≤ G to mean that H is a subgroup of G, and N G to mean that N is a normal subgroup of G. If E/F and K/F are two field extensions, then when we say that K/F is contained in E/F , we mean via a homomorphism that fixes F. We assume the following basic facts in this set...

In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schrödinger type. From these equ...

In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...

in this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. we establishthe orthogonality relations for square integrable representationsof homogeneous spaces which give rise to the existence of aunique self adjoint positive operator on the set of admissiblewavelets. finally, we show that this operator is a constant multiple of identity operator...

The aim of the present study was to investigate the relationship between the polar surface area and other molecular properties of the model drugs and their transdermal permeability across the rat skin. Few model drugs which are weakly acidic (ibuprofen, aceclofenac and glipizide) and weakly basic (olanzapine, telmisartan and sildenafil citrate) were selected for the study based on Polar surface...

From an abstract algebraic perspective, an explanation for this can be given as follows: since √ D is irrational, the polynomial t −D is irreducible over Q. Since the ring Q[t] is a PID, the irreducible element t − D generates a maximal ideal (t−D), so that the quotient Q[t]/(t−D) is a field. Moreover, the map Q[ √ D]→ Q[t]/(t −D) which is the identity on Q and sends √ D 7→ t is an isomorphism ...

Let A be a Dedekind domain whose field of fractions K is a global field. Let p be a non-zero prime ideal of A, and Kp the completion of K at p. The Montes algorithm factorizes a monic irreducible separable polynomial f(x) ∈ A[x] over Kp, and it provides essential arithmetic information about the finite extensions of Kp determined by the different irreducible factors. In particular, it can be us...

In this paper, we are interested in the question of separating two characters of the absolute Galois group of a number field K, by the Frobenius of a prime ideal p of OK . We first recall an upper bound for the norm N(p) of the smallest such prime p, depending on the conductors and on the degrees. Then we give two applications: (i) find a prime number p for which P (mod p) has a certain type of...

We discuss the issue of multiplicity of the BPS states in (1+1)-dimensional models with minimal N=1 supersymmetry. The previous argument that the irreducible representation of supersymmetry algebra is one-dimensional in this case is elaborated. Algebraic treatment is illustrated by explicit quasiclassical quantization in various weakly coupled models which present examples of oneand two-dimensi...