Copolymers, particularly Pluronics®, are typically used to sterically stabilise colloidal nanostructured particles composed of a lyotropic liquid crystalline bicontinuous cubic phase (cubosomes). There is a need to design and assess new functionalisable stabilisers for these colloidal drug delivery systems. Six amphiphilic brush copolymers, poly(octadecyl acrylate)-block-poly(polyethylene glyco...

A Recursive form cubic B-spline basis function is used as basis in B-spline collocation method to solve second linear singularly perturbed two point boundary value problem. The performance of the method is tested by considering the numerical examples with different boundary conditions. Results of numerical examples show the robustness of the method when compared with the analytical solution.

Let X ⊂ P be a geometrically integral cubic hypersurface defined over Q, with singular locus of dimension 6 dimX − 4. Then the main result in this paper is a proof of the fact that X(Q) contains Oε,X(B ) points of height at most B.

We shall show that the three variable cubic inequality t(a + b + c) + (t − 2t)(ab + bc + ca) ≥ (2t − 1)(ab + bc + ca) + (3t − 6t + 3t − 6t + 3)abc holds for non-negative a, b, c, and for any real number t. We also show some similar three variable cyclic quartic inequalities.

The existence of a primitive free (normal) cubic x3− ax2 + cx− b over a finite field F with arbitrary specified values of a (6= 0) and b (primitive) is guaranteed. This is the most delicate case of a general existence theorem whose proof is thereby completed.

Polyethylene oxide –b– polypropylene oxide -bpolyethylene oxide (EO106PO70EO106) block copolymer self-organizes into polymeric supramolecules, characterized by NMR as phase transition from the isotropic stack-up block structure to the ordered cubic polymeric supramolecular structure. Its dependence on both temperature and copolymer concentration is clearly shown by the changes in line shape and...

In this short note we would like to show the relation between the cubic open string field theory for N D-instantons and the string field theory in the presence of the background B field.

We study quantum interference effects due to electron motion on a three-dimensional cubic lattice in a continuously tunable magnetic field B of arbitrary orientation and magnitude. These effects arise from the interference between magnetic phase factors associated with different electron closed paths. The sums of these phase factors, called lattice path integrals, are many-loop generalizations ...

Let K,L,M be orthogonal projections of a point P onto the sides of a triangle ABC. Then the locus of P such that K,L,M are collinear, is the circumcircle of ABC. This theorem has several generalizations [4], [5], [10],[6], [7], [9]. A generalization of the Simson–Wallace theorem which is by [2] ascribed to J. D. Gergonne is as follows: Let K,L,M be orthogonal projections of a point P onto the s...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...