Iranian Mathematical Society
Journal of the Iranian Mathematical Society
2717-1612
2
1
2021
03
01
Sanov's theorem on Lie relators in groups of exponent $p$
1
16
EN
M.
Vaughan-Lee
Christ Church, University of Oxford,
Oxford, OX1 1DP, England.
michael.vaughan-lee@chch.ox.ac.uk
10.30504/jims.2020.110856
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.
Sanov's theorem,Lie relators,Groups of exponent $p$
http://jims.ims.ir/article_110856.html
http://jims.ims.ir/article_110856_87c80830a05958c113d30d5f05f1c835.pdf
Iranian Mathematical Society
Journal of the Iranian Mathematical Society
2717-1612
2
1
2021
03
01
Generalized trapezoid type inequalities for functions with values in Banach spaces
17
38
EN
S.
S.
Dragomir
Victoria University, Melbourne, Australi
sever.dragomir@vu.edu.au
10.30504/jims.2021.299742.1038
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],<br />‖(∫_{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} <br />×(∫_{a}^{b}‖Y′(t)‖^{q}dt)^{1/q}<br /><br />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.
Banach spaces,integral inequalities,Operator monotone functions
http://jims.ims.ir/article_138341.html
http://jims.ims.ir/article_138341_5a034622d668c9097177e956cd4e849e.pdf
Iranian Mathematical Society
Journal of the Iranian Mathematical Society
2717-1612
2
1
2021
03
01
On a Hilbert-type integral inequality in the whole plane
39
51
EN
M.
Th.
Rassias
Department of Mathematics and Engineering Sciences,
Hellenic Military Academy,
16673 Vari Attikis, Greece
mthrassias@yahoo.com
B.
Yang
Department of Mathematics, Guangdong University of
Education, Guangzhou, Guangdong
510303, P. R. China
bcyang@gdei.edu.cn
G.
C.
Meletiou
University of Ioannina, Ioannina, Greece.
meletiu@gmail.com
10.30504/jims.2021.309063.1044
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.
Hilbert-type integral inequality,weight function,parameter,equivalent form,operator
http://jims.ims.ir/article_141199.html
http://jims.ims.ir/article_141199_a726440e0929ea956c8fa65786aab4ca.pdf
Iranian Mathematical Society
Journal of the Iranian Mathematical Society
2717-1612
2
1
2021
03
01
The first eigenvalue of $left(p,qright)$-elliptic quasilinear system along the Ricci flow
53
70
EN
S.
Azami
Department of pure mathematics, Faculty of mathematical science, Imam Khomeini international university, Qazvin, Iran
azami@sci.ikiu.ac.ir
M.
Habibi Vosta Kolaei
Department of pure mathematics, Faculty of science, Imam Khomeini international university, Qazvin, Iran
mj.habibi@edu.ikiu.ac.ir
10.30504/jims.2021.263742.1026
In this paper we investigate the monotonicity of the first eigenvalue of $left(p,qright)$-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.
Ricci flow,$(p,q)$-elliptic quasilinear system,Eigenvalue
http://jims.ims.ir/article_141490.html
http://jims.ims.ir/article_141490_c8292bfa33955943da919d35e5f22c90.pdf