Sanov's theorem on Lie relators in groups of exponent $p$
M.
Vaughan-Lee
Christ Church, University of Oxford,
Oxford, OX1 1DP, England.
author
text
article
2021
eng
I give a proof of Sanov's theorem that the Lie relators of weight at most $2p-2$ in groups of exponent $p$ are consequences of the identity $px=0$ and the $(p-1)$-Engel identity. This implies that the order of the class $2p-2$ quotient of the Burnside group $B(m,p)$ is the same as the order of the class $2p-2$ quotient of the free $m$ generator $(p-1)$-Engel Lie algebra over GF$(p)$. To make the proof self-contained I have also included a derivation of Hausdorff's formulation of the Baker Campbell Hausdorff formula.
Journal of the Iranian Mathematical Society
Iranian Mathematical Society
2717-1612
2
v.
1
no.
2021
1
16
http://jims.ims.ir/article_110856_87c80830a05958c113d30d5f05f1c835.pdf
dx.doi.org/10.30504/jims.2020.110856
Generalized trapezoid type inequalities for functions with values in Banach spaces
S.
Dragomir
Victoria University, Melbourne, Australi
author
text
article
2021
eng
Let E be a complex Banach space. In this paper we show among others that, if α:[a,b]→C is continuous and Y:[a,b]→E is strongly differentiable on the interval (a,b), then for all u∈[a,b],‖(∫_{u}^{b}α(s)ds)Y(b)+(∫_{a}^{u}α(s)ds)Y(a)-∫_{a}^{b}α(t)Y(t)dt‖ ≤{┊max{∫_{u}^{b}|α(s)|ds,∫_{a}^{u}|α(s)|ds}∫_{a}^{b}‖Y′(t)‖dt, [∫_{u}^{b}(b-t)|α(t)|dt+∫_{a}^{u}(t-a)|α(t)|dt]sup_{t∈[a,b]}‖Y′(t)‖, ≤(b-a)^{1/p}[(∫_{u}^{b}|α(s)|ds)^{p}+(∫_{a}^{u}|α(s)|ds)^{p}]^{1/p} ×(∫_{a}^{b}‖Y′(t)‖^{q}dt)^{1/q}for p, q>1 with (1/p)+(1/q)=1. Applications for operator monotone functions with examples for power and logarithmic functions are also given.
Journal of the Iranian Mathematical Society
Iranian Mathematical Society
2717-1612
2
v.
1
no.
2021
17
38
http://jims.ims.ir/article_138341_5a034622d668c9097177e956cd4e849e.pdf
dx.doi.org/10.30504/jims.2021.299742.1038
On a Hilbert-type integral inequality in the whole plane
M.
Rassias
Department of Mathematics and Engineering Sciences,
Hellenic Military Academy,
16673 Vari Attikis, Greece
author
B.
Yang
Department of Mathematics, Guangdong University of
Education, Guangzhou, Guangdong
510303, P. R. China
author
G.
Meletiou
University of Ioannina, Ioannina, Greece.
author
text
article
2021
eng
Using weight functions and techniques of real analysis, a new Hilbert-type integral inequality in the whole plane with nonhomogeneous kernel and a best possible constant factor is proved. Equivalent forms, several particular inequalities and operator expressions are considered.
Journal of the Iranian Mathematical Society
Iranian Mathematical Society
2717-1612
2
v.
1
no.
2021
39
51
http://jims.ims.ir/article_141199_a726440e0929ea956c8fa65786aab4ca.pdf
dx.doi.org/10.30504/jims.2021.309063.1044
The first eigenvalue of $\left(p,q\right)$-elliptic quasilinear system along the Ricci flow
S.
Azami
Department of pure mathematics, Faculty of mathematical science, Imam Khomeini international university, Qazvin, Iran
author
M.
Habibi Vosta Kolaei
Department of pure mathematics, Faculty of science, Imam Khomeini international university, Qazvin, Iran
author
text
article
2021
eng
In this paper we investigate the monotonicity of the first eigenvalue of $\left(p,q\right)$-elliptic quasilinear systems along the Ricci flow in both normalized and unnormalized conditions. In particular, we study the eigenvalue problem for this system in the case of Bianchi classes for $3$-homogeneous manifolds.
Journal of the Iranian Mathematical Society
Iranian Mathematical Society
2717-1612
2
v.
1
no.
2021
53
70
http://jims.ims.ir/article_141490_c8292bfa33955943da919d35e5f22c90.pdf
dx.doi.org/10.30504/jims.2021.263742.1026