Loop group and homotopy class as additive group

2021 ◽  
Vol 15 (8) ◽  
pp. 373-381
Author(s):  
Toru Shimizu
Keyword(s):  
Homotopy Class ◽  
Additive Group ◽  
Loop Group

scholarly journals Finite skew braces with solvable additive group

2021 ◽  
Vol 574 ◽  
pp. 172-183
Author(s):  
Ilya Gorshkov ◽  
Timur Nasybullov
Keyword(s):  
Additive Group

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

scholarly journals On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 605
Author(s):  
Da-Zhi Sun ◽  
Ji-Dong Zhong ◽  
Hong-De Zhang ◽  
Xiang-Yu Guo
Keyword(s):  
Electronic Devices ◽  
Additive Group ◽  
Fixed Number ◽  
Scalar Multiplication ◽  
Computation Cost ◽  
Public Key Cryptosystems ◽  
Adaptive Window ◽  
Computation Efficiency ◽  
Window Method ◽  
Constrained Environments

A basic but expensive operation in the implementations of several famous public-key cryptosystems is the computation of the multi-scalar multiplication in a certain finite additive group defined by an elliptic curve. We propose an adaptive window method for the multi-scalar multiplication, which aims to balance the computation cost and the memory cost under register-constrained environments. That is, our method can maximize the computation efficiency of multi-scalar multiplication according to any small, fixed number of registers provided by electronic devices. We further demonstrate that our method is efficient when five registers are available. Our method is further studied in detail in the case where it is combined with the non-adjacent form (NAF) representation and the joint sparse form (JSF) representation. One efficiency result is that our method with the proposed improved NAF n-bit representation on average requires 209n/432 point additions. To the best of our knowledge, this efficiency result is optimal compared with those of similar methods using five registers. Unlike the previous window methods, which store all possible values in the window, our method stores those with comparatively high probabilities to reduce the number of required registers.

scholarly journals Comparison of the clinical outcomes of skin bridge loop ileostomy and traditional loop ileostomy in patients with low rectal cancer

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hui Ye ◽  
Shujuan Huang ◽  
Jie Yu ◽  
Qichang Zhou ◽  
Changlei Xi ◽  
...  
Keyword(s):  
Rectal Cancer ◽  
Low Anterior Resection ◽  
Clinical Evidence ◽  
Loop Ileostomy ◽  
Loop Group ◽  
Clinical Results ◽  
Low Rectal Cancer ◽  
Analog Scale ◽  
Traditional Group ◽  
Bridge Group

AbstractTo compare the clinical results of patients with low rectal cancer who underwent skin bridge loop ileostomy and traditional loop ileostomy, and provide clinical evidence for choosing a better ostomy method. We retrospectively collected data of 118 patients with rectal cancer who underwent low anterior resection and loop ileostomy. To investigate the patients characteristics, postoperative stoma-related complications and the frequency of exchanged ostomy bags. The differences of these indicators between the two groups of patients who underwent skin bridge loop ileostomy and traditional loop ileostomy were compared. The Visual Analog Scale (VAS) score of the skin bridge loop ileostomy group was lower than that of the traditional ileostomy loop group (P < 0.05). The skin bridge group had a lower Discoloration, Erosion, Tissue overgrowth (DET) score and incidence of mucocutaneous separation than the traditional group at the 1st and 2nd weeks after operation (P < 0.05). The average number of weekly exchanged ostomy bags was significantly less in the skin bridge group than in the traditional group within 4 weeks after surgery (P < 0.05). Our experience demonstrates that the skin bridge loop ileostomy may significantly reduce early postoperative stoma-related complications, the frequency of exchanged ostomy bags and patients’ medical costs after discharge.

scholarly journals SMALL VALUE ESTIMATES FOR THE ADDITIVE GROUP

2010 ◽  
Vol 06 (04) ◽  
pp. 919-956 ◽  
Author(s):  
DAMIEN ROY
Keyword(s):  
Algebraic Independence ◽  
Additive Group

We generalize Gel'fond's criterion for algebraic independence to the context of a sequence of polynomials whose first derivatives take small values on large subsets of a fixed subgroup of ℂ, instead of just one point (one extension deals with a subgroup of ℂ×).

CANCELLATION LAW AND UNIQUE FACTORIZATION THEOREM FOR STRING OPERATIONS

2006 ◽  
Vol 05 (02) ◽  
pp. 231-243
Author(s):  
DONGVU TONIEN
Keyword(s):  
Abelian Group ◽  
Algebraic Structure ◽  
Additive Group ◽  
New Product ◽  
Binary String ◽  
Factorization Theorem ◽  
General Criterion ◽  
Unique Factorization ◽  
Product Operation ◽  
Associative Law

Recently, Hoit introduced arithmetic on blocks, which extends the binary string operation by Jacobs and Keane. A string of elements from the Abelian additive group of residues modulo m, (Zm, ⊕), is called an m-block. The set of m-blocks together with Hoit's new product operation form an interesting algebraic structure where associative law and cancellation law hold. A weaker form of unique factorization and criteria for two indecomposable blocks to commute are also proved. In this paper, we extend Hoit's results by replacing the Abelian group (Zm, ⊕) by an arbitrary monoid (A, ◦). The set of strings built up from the alphabet A is denoted by String(A). We extend the operation ◦ on the alphabet set A to the string set String(A). We show that (String(A), ◦) is a monoid if and only if (A, ◦) is a monoid. When (A, ◦) is a group, we prove that stronger versions of a cancellation law and unique factorization hold for (String(A), ◦). A general criterion for two irreducible strings to commute is also presented.

SIMPLE 4-KNOTS

1998 ◽  
Vol 07 (07) ◽  
pp. 907-923
Author(s):  
J. A. HILLMAN ◽  
C. KEARTON
Keyword(s):  
Homotopy Class ◽  
Torsion Free

We show that the isotopy type of a 1-simple n-knot K is determined by the Postnikov (n - 1)-stage of its exterior X(K), together with the homotopy class of the longitude λK ∈ πn(X(K)). Moreover any pair (X, j) where X is a 4-dimensional homology circle with π1(X) ≅ Z and j : S4 × S1 → X is such that (X, j) = (MCyl(j), S4 × S1) is an orientable PD6-pair is realizable by some simple 4-knot. We derive complete algebraic characterizations of torsion free fibred simple 4-knots and of Artin spins of fibred simple 3-knots.

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