The transition from subcritical to supercritical stationary periodic patterns is described by the one-dimensional cubic-quintic Ginzburg-Landau equation A(t) = μA + A(xx) + i(a(1)|A|(2)A(x) + a(2)A(2)A(x)*) + b|A|(2)|A - |A|(4)A, where A(x,t) represents the pattern amplitude and the coefficients μ, a(1), a(2), and b are real. The conditions for Eckhaus instability of periodic solutions are dete...

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic B-splines as weight functions has been developed to solve a general seventh order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet and ...

We use the Shokurov connectedness principle and the Corti inequality to prove the birational superrigidity of a nodal hypersurface in P 5 of degree 5. We assume that all varieties are projective, normal and defined over C.

A. Carpi (1993) and A. Lepistö (1993) proved independently that smooth words are cube-free for the alphabet {1, 2}, but nothing is known on whether for the other 2-letter alphabets, smooth words are k-power-free for some suitable positive integer k. This paper establishes the derivative formula (Theorem 10) of the concatenation of two smooth words and power derivative formula of smooth words ov...

A bstract Ricci flat metrics for Calabi-Yau threefolds are not known analytically. In this work, we employ techniques from machine learning to deduce numerical K3, the Fermat quintic, and Dwork quintic. This investigation employs a simple, modular neural network architecture that is capable of approximating Kähler manifolds dimensions two three. We show measures assess flatness consistency metr...

In this paper, we use the Mellin-Barnes-Watson method to relate solutions of a certain type $q$-difference equations at $Q=0$ and $Q=\infty$. We consider two special cases; first is equation $K$-theoretic $I$-function quintic, which degree 25; Adams' find extra 20 $Q=0$. The second case fuchsian case, confluent differential cohomological quintic. compute connection matrix study confluence struc...

The modified equal width (MEW) equation arising from the nonlinear media with dispersion process has been paid special attention in the past decades [1, 2, 3, 4, 5]. Since its wide applications and important mathematical properties, many methods have been presented to study the different solutions and physical phenomena related to this equation. By using the Petrov-Galerkin method together with...

We revisit type I compactifications with a Spin(32)/Z2 gauge bundle that admits no vector structure. We elucidate the relation of this Z2 obstruction to discrete B-field flux and to ’t Hooft flux and clarify some subtleties in the T-duality transformation to type IIA intersecting D-brane models. We reexamine the earliest 3-generation GUT model on magnetized D-branes and show its consistency whe...

This paper deals with a finite element method involving Petrov-Galerkin method with cubic B-splines as basis functions and quintic B-splines as weight functions to solve a general fourth order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet type of boundary ...