Dokuchaev, Mikhailo Khrypchenko, Mykola Makuta, Mayumi
Published in
Forum Mathematicum

We introduce the concept of a partial abstract kernel associated to a group G and a semilattice of groups A and relate the partial cohomology group H 3 ( G , C ( A ) ) {H^{3}(G,C(A))} with the obstructions to the existence of admissible extensions of A by G which realize the given abstract kernel. We also show that if such extensions exist, the...

Iriye, Kouyemon Kishimoto, Daisuke Levi, Ran
Published in
Forum Mathematicum

A generalised Postnikov tower for a space X is a tower of principal fibrations with fibres generalised Eilenberg–MacLane spaces, whose inverse limit is weakly homotopy equivalent to X. In this paper we give a characterisation of a polyhedral product Z K ( X , A ) {Z_{K}(X,A)} whose universal cover either admits a generalised Postnikov tower of fi...

Naik, Tushar Kanta Nanda, Neha Singh, Mahender
Published in
Forum Mathematicum

The twin group T n {T_{n}} is a right-angled Coxeter group generated by n - 1 {n-1} involutions, and the pure twin group PT n {\mathrm{PT}_{n}} is the kernel of the natural surjection from T n {T_{n}} onto the symmetric group on n symbols. In this paper, we investigate some structural aspects of these groups. We derive a formula for the number of c...

Park, Euisung
Published in
Forum Mathematicum

Classical Castelnuovo Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension c is at most ( c + 1 2 ) {{{c+1}\choose{2}}} and the equality is attained if and only if the variety is of minimal degree. Also G. Fano’s generalization of Castelnuovo Lemma implies that the ...

Zaprawa, Paweł
Published in
Forum Mathematicum

In this paper we discuss coefficient problems for functions in the class 𝒞 0 ( k ) {{\mathcal{C}}_{0}(k)} . This family is a subset of 𝒞 {{\mathcal{C}}} , the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive ...

Bulacu, Daniel Torrecillas, Blas
Published in
Forum Mathematicum

We prove a uniqueness type theorem for (weak, total) integrals on a Frobenius cowreath in a monoidal category. When the cowreath is, moreover, pre-Galois, we construct a Morita context relating the subalgebra of coinvariants and a certain wreath algebra. Then we see that the strictness of the Morita context is related to the Galois property of the ...

Doucha, Michal
Published in
Forum Mathematicum

The aim of this note is to correct the proof of Proposition 2.15 in the original article [M. Doucha, Metrical universality for groups, Forum Math. 29 2017, 4, 847–872].

Gao, Chuanwei Miao, Changxing Yang, Jianwei-Urbain
Published in
Forum Mathematicum

In this paper, we establish an improved variable coefficient version of the square function inequality, by which the local smoothing estimate L α p → L p {L^{p}_{\alpha}\to L^{p}} for the Fourier integral operators satisfying cinematic curvature condition is further improved. In particular, we establish almost sharp results for 2

Spirito, Dario
Published in
Forum Mathematicum

We study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a na...

Vignatti, Maria Amelia Salinas, Oscar Hartzstein, Silvia
Published in
Forum Mathematicum

We introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on t...