Integral formula for a generalized Sato-Levine invariant in magnetic hydrodynamics

Mathematical Notes - For a pair of divergence-free vector fields B and $$ \tilde B $$ respectively localized in two oriented tubes U and $$ \tilde U $$ in ?3, we propose a fourth-order...     

A Note on 3-Divisibility of Class Number of Quadratic Field

In this paper, the authors show that there exists infinitely many family of pairs of quadratic fields Q(D^1/2) and Q((D+n)(1/2)) with D, n∈Z whose class numbers are both divisible by 3.     

A family of pairs of imaginary cyclic fields of degree $$(p-1)/2$$(p-1)/2 with both class numbers divisible by p

The Ramanujan Journal - Let p be a prime number with $$p\equiv 5\ (\mathrm{mod}\ {8})$$. We construct a new infinite family of pairs of imaginary cyclic fields of degree $$(p-1)/2$$ with both class...     

Nonautonomous vector fields on $$S^3$$ : Simple dynamics and wild embedding of separatrices

Theoretical and Mathematical Physics - We construct new substantive examples of nonautonomous vector fields on a $$3$$ -dimensional sphere having simple dynamics but nontrivial topology. The...     

On a Diophantine equation involving primes

The Ramanujan Journal - For all positive integers k and N, we prove that there are infinitely many totally real multiquadratic fields K of degree $$2^k$$ over $$\mathbb {Q}$$ such that each...     

A two-weight Sobolev inequality for Carnot-Carathéodory spaces

Ricerche di Matematica - Let $$X = \{X_1,X_2, \ldots ,X_m\}$$ be a system of smooth vector fields in $${{\mathbb R}^n}$$ satisfying the Hörmander’s finite rank condition. We prove the...     

Some remarks on Kida’s formula when $$\mu \ne 0$$ μ ≠ 0

The Ramanujan Journal - Kida’s formula in classical Iwasawa theory relates the Iwasawa $$\lambda $$ -invariants of p-extensions of number fields. Analogue of this formula was subsequently...     

Covers of Point-Hyperplane Graphs

A cover of the non-incident point-hyperplane graph of projective dimension 3 for fields of characteristic 2 is constructed. For fields of even order larger than 2, this leads to an elementary construction of the non-split extension of SL₄( )by ⁶.     

Construction of LDPC convolutional codes via difference triangle sets

Designs, Codes and Cryptography - In this paper, a construction of $$(n,k,\delta )$$ LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and...     

High order elements in finite fields arising from recursive towers

Designs, Codes and Cryptography - We illustrate a general technique to construct towers of fields producing high order elements in $$\mathbb {F}_{q^{2^n}}$$ , for odd q, and in $$\mathbb {F}_{2^{2...     

Frobenius semisimplicity for convolution morphisms

Mathematische Zeitschrift - This article concerns properties of mixed $$\ell $$ -adic complexes on varieties over finite fields, related to the action of the Frobenius automorphism. We establish a...     

Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree

Theoretical and Mathematical Physics - We study the Potts model in translation-invariant and periodic external fields on the Cayley tree of order $${k\geq 2}$$ . For the Potts model in a...     

Unit groups of some multiquadratic number fields and 2-class groups

Periodica Mathematica Hungarica - Let $$p\equiv -q \equiv 5\pmod 8$$ be two prime integers. In this paper, we investigate the unit groups of the fields $$ L_1 =\mathbb {Q}(\sqrt{2}, \sqrt{p},...     

Randomized consistent statistical inference for random processes and fields

Statistical Inference for Stochastic Processes - We propose a randomized approach to the consistent statistical analysis of random processes and fields on $${\mathbb {R}}^m$$ and $${\mathbb {Z}}^m,...     

A parameterized family of quadratic class groups with 3-Sylow subgroups of rank at least three

The Ramanujan Journal - In a recent paper, Kishi and Komatsu have shown that the complex quadratic fields of discriminant $$\begin{aligned} \Delta _{18} = 4 - 3^{18n+3} \end{aligned}$$ have a class...     

Minimization over the $$\ell _1$$ -ball using an active-set non-monotone projected gradient

Computational Optimization and Applications - The $$\ell _1$$ -ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis)...     

Class number one problem for the real quadratic fields $${{\mathbb {Q}({\sqrt{m^2+2r}})}}$$ Q ( m 2 + 2 r )

Archiv der Mathematik - We investigate the class number one problem for a parametric family of real quadratic fields of the form $$\mathbb {Q}( \sqrt{m^2+4r})$$ for certain positive integers m and r.