S. L. Narasimhan, Joseph A. Nathan, P. S. R. Krishna and K. P. N. Murthy Solid State Physics Division, Reactor Physics Design Division Bhabha Atomic Research Centre, Mumbai-400085, India. Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamilnadu, India. Abstract We formulate a mean-field-like theory of long-range correlated L-alphabets sequences, which ar...

Abstract For a smooth rigid space X over perfectoid field extension K of $\mathbb {Q}_p$ , we investigate how the v -Picard group associated diamond $X^{\diamondsuit }$ differs from analytic Picard . To this end, construct left-exact ‘Hodge–Tate logarithm’ sequence $$\begin{align*}0\to \operatorname{Pic}_{\mathrm{an}}(X)\to \operatorname{Pic}_v(X^{\diamondsuit})\to H^0(X,\Omega_X^1)\{-1\}. \end...

Let $p \geq 2$ be a prime, and $\mathbb{F}_p$ the field with $p$ elements. Extending result of Seidel for $p=2,$ we construct an isomorphism between Floer cohomology exact or Hamiltonian symplectomorphism $\phi,$ coefficients, $\mathbb{Z}/p \mathbb{Z}$-equivariant Tate its $p$-th power $\phi^p.$ The construction involves Kaledin-type quasi-Frobenius map, as well pants product: equivariant opera...

In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation...

Adin, Brenti, and Roichman introduced the pairs of statistics (ndes, nmaj) and (fdes, fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group Bn, and can be considered “Euler-Mahonian” in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, along...