oCLP surfaces with orthorhombic distortion (OCLP for short) are a fattily of twoparameter triply periodic embedded minimal surfaces. We show that they correspond to the Weierstrass function of the form ~

In this paper, we derive a canonical representation for the first order hyperbolic equation systems with their coefficient matrices satisfying the Clifford algebra Cl(1, 3), and then demonstrate some of its applications. This canonical formalism can naturally give a unified description for the fundamental fields in physics. PACS numbers: 11.10.-z, 11.10.Cd, 12.10.-g

The approximation of the normal distribution by means of a chaotic expression is achieved by means of Weierstrass function, where, for a certain set of parameters, the density of the derived recurrence renders good approximation of the bell curve.

Helton and Vinnikov proved that every hyperbolic ternary form admits a symmetric derminantal representation via Riemann theta functions. In the case the algebraic curve of the hyperbolic ternary form is elliptic, the determinantal representation of the ternary form is formulated by using Weierstrass ℘-functions in place of Riemann theta functions. An example of this approach is given.

We derive the complete (curvature) terms of effective D-brane actions, for arbitrary ambient geometries and world-volume embeddings, at lowest order (disk-level) in the string-loop expansion. These terms reproduce the o(α′ ) corrections to string scattering amplitudes, and are consistent with duality conjectures. In the particular case of the D3-brane with trivial normal bundle, considerations ...

In a recent paper by M. Wieczorek, a claim is made regarding the possible rational torsion subgroups of elliptic curves E/Q in short Weierstrass form, subject to certain inequalities for their coefficients. We provide a series of counterexamples to this claim and explore a number of related results. In particular, we show that, for any ε > 0, all but finitely many curves EA,B : y 2 = x +Ax+B, w...

A minor error in the necessary conditions for the algebraic form of the Lamé equation to have a finite projective monodromy group, and hence for it to have only algebraic solutions, is pointed out. [See F. Baldassarri, “On algebraic solutions of Lamé’s differential equation”, J. Differential Equations 41 (1) (1981), 44–58.] It is shown that if the group is the octahedral group , then the degree...