The diagnosability of Möbius cubes for the g-extra condition

2022 ◽  
Author(s):  
Shiying Wang
Keyword(s):  
Extra Condition

scholarly journals Retraction of the paper entitled “Lepton number violation in a unified framework“

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Apriadi Salim Adam ◽  
Yuta Kawamura ◽  
Yamato Matsuo ◽  
Takuya Morozumi ◽  
Yusuke Shimizu ◽  
...  
Keyword(s):  
Mass Function ◽  
Lepton Number ◽  
Primordial Black Hole ◽  
Unified Framework ◽  
Extra Condition ◽  
Formal Expression ◽  
Lepton Number Violation ◽  
Standard Criterion ◽  
New Criterion ◽  
New Formula

Abstract Computations of the primordial black hole (PBH) mass function discussed in the literature have conceptual issues. They stem from the fact that the mass function is a differential quantity and the standard criterion of the PBH formation from the seed primordial fluctuations cannot be directly applied to the computation of the differential quantities. We propose a new criterion of the PBH formation, which is the addition of one extra condition to the existing one. By doing this, we derive a formal expression of the PBH mass function without introducing any ambiguous interpretations that exist in the previous studies. Once the underlying primordial fluctuations are specified, the PBH mass function can be in principle determined by the new formula. As a demonstration of our formulation, we compute the PBH mass function analytically for the case where the perturbations are Gaussian and the space is 1 dimension.

scholarly journals Infinitely many equivalent versions of the graceful tree conjecture

2015 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Tao-Ming Wang ◽  
Cheng-Chang Yang ◽  
Lih-Hsing Hsu ◽  
Eddie Cheng
Keyword(s):  
Perfect Matching ◽  
Absolute Difference ◽  
Extra Condition ◽  
Graceful Labeling ◽  
The Absolute

A graceful labeling of a graph with q edges is a labeling of its vertices using the integers in [0, q], such that no two vertices are assigned the same label and each edge is uniquely identified by the absolute difference between the labels of its endpoints. The well known Graceful Tree Conjecture (GTC) states that all trees are graceful, and it remains open. It was proved in 1999 by Broersma and Hoede that there is an equivalent conjecture for GTC stating that all trees containing a perfect matching are strongly graceful (graceful with an extra condition). In this paper we extend the above result by showing that there exist infinitely many equivalent versions of the GTC. Moreover we verify these infinitely many equivalent conjectures of GTC for trees of diameter at most 7. Among others we are also able to identify new graceful trees and in particular generalize the ?-construction of Stanton-Zarnke (and later Koh- Rogers-Tan) for building graceful trees through two smaller given graceful trees.

scholarly journals Relative injectivity and CS-modules

1994 ◽  
Vol 17 (4) ◽  
pp. 661-666
Author(s):  
Mahmoud Ahmed Kamal
Keyword(s):  
Direct Decomposition ◽  
Injective Hull ◽  
Extra Condition ◽  
Direct Sums ◽  
Direct Sum ◽  
Injective Modules ◽  
Semisimple Module ◽  
Continuous Module

In this paper we show that a direct decomposition of modulesM⊕N, withNhomologically independent to the injective hull ofM, is a CS-module if and only ifNis injective relative toMand both ofMandNare CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for quasi-injective modules. But when we confine ourselves to CS-modules we need no conditions on their socles. Then we investigate direct sums of CS-modules which are pairwise relatively inective. We show that every finite direct sum of such modules is a CS-module. This result is known for quasi-continuous modules. For the case of infinite direct sums, one has to add an extra condition. Finally, we briefly discuss modules in which every two direct summands are relatively inective.

Extension of Zelazko’s theorem to n-Jordan homomorphisms

2019 ◽  
Vol 10 (2) ◽  
pp. 165-170 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Hülya İnceboz
Keyword(s):  
Extra Condition ◽  
Jordan Homomorphisms

Abstract In this article, we correct the proof of the main theorem of Gordji’s paper [M. Eshaghi Gordji, n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 2009, 1, 159–164] by a different method and generalize Zelazko’s theorem to 4-Jordan homomorphisms by considering an extra condition.

The seven circles theorem revisited

2018 ◽  
Vol 102 (554) ◽  
pp. 280-301 ◽  
Author(s):  
John R. Silvester
Keyword(s):  
Extra Condition ◽  
Base Points ◽  
Base Circle ◽  
A Chain

The circles C1, & , Cn form a chain of length n if Ci touches Ci + 1, for i = 1, & , n − 1, and the chain is closed if also Cn touches C1. A cyclic chain is a chain for which all the circles touch another circle S, the base circle of the chain. If Ci touches S at Pi, then P1, & , Pn are the base points of the chain. Sometimes there may be coincidences among the base points; in particular, if Pi = Pj, then the line PiPj should be interpreted as the tangent S to at Pi.The seven circles theorem first appeared in [1, §3.1], and some historical details of its genesis can be found in John Tyrrell's obituary [2]. The theorem concerns a closed cyclic chain of length 6, and says that, if a certain extra condition is satisfied, then the lines P1P4, P2P5, P3P6 joining opposite base points are concurrent. Here and throughout, ‘concurrent’ should be read as ‘concurrent or all parallel’, that is, the point of concurrency might be at infinity.

scholarly journals A Sharp Bound on RIC in Generalized Orthogonal Matching Pursuit

2018 ◽  
Vol 61 (1) ◽  
pp. 40-54 ◽  
Author(s):  
Wengu Chen ◽  
Huanmin Ge
Keyword(s):  
Matching Pursuit ◽  
Natural Extension ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal ◽  
Sparse Signals ◽  
Sensing Matrix ◽  
Extra Condition ◽  
Exact Reconstruction ◽  
Restricted Isometry Constant ◽  
Generalized Orthogonal

AbstractThe generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of the orthogonal matching pursuit (OMP). It is used to recover sparse signals in compressive sensing. In this paper, a new bound is obtained for the exact reconstruction of every K-sparse signal via the gOMP algorithm in the noiseless case. That is, if the restricted isometry constant (RIC) δNK+1 of the sensing matrix A satisfiesthen the gOMP can perfectly recover every K-sparse signal x from y = Ax. Furthermore, the bound is proved to be sharp. In the noisy case, the above bound on RIC combining with an extra condition on the minimum magnitude of the nonzero components of K-sparse signals can guarantee that the gOMP selects all of the support indices of the K-sparse signals.

scholarly journals State sum construction of two-dimensional topological quantum field theories on spin surfaces

2015 ◽  
Vol 24 (05) ◽  
pp. 1550028 ◽  
Author(s):  
S. Novak ◽  
I. Runkel
Keyword(s):  
Spin Structure ◽  
Topological Field Theory ◽  
Quantum Field Theories ◽  
Extra Condition ◽  
Admissibility Condition ◽  
Topological Quantum ◽  
Combinatorial Model ◽  
Topological Field ◽  
Pachner Moves ◽  
Combinatorial Data

We provide a combinatorial model for spin surfaces. Given a triangulation of an oriented surface, a spin structure is encoded by assigning to each triangle a preferred edge, and to each edge an orientation and a sign, subject to certain admissibility conditions. The behavior of this data under Pachner moves is then used to define a state sum topological field theory on spin surfaces. The algebraic data is a Δ-separable Frobenius algebra whose Nakayama automorphism is an involution. We find that a simple extra condition on the algebra guarantees that the amplitude is zero unless the combinatorial data satisfies the admissibility condition required for the reconstruction of the spin structure.

An inexact algorithm with proximal distances for variational inequalities

2018 ◽  
Vol 52 (1) ◽  
pp. 159-176 ◽  
Author(s):  
E.A. Papa Quiroz ◽  
L. Mallma Ramirez ◽  
P.R. Oliveira
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Proximal Point Algorithm ◽  
Convergence Properties ◽  
Proximal Point ◽  
Extra Condition ◽  
Bregman Distances ◽  
Optim Theory ◽  
Inexact Proximal ◽  
Inexact Algorithm

In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generated by the algorithm is convergent for the pseudomonotone case and assuming an extra condition on the solution set we prove the convergence for the quasimonotone case. This approach unifies the results obtained by Auslender et al. [Math Oper. Res. 24 (1999) 644–688] and Brito et al. [J. Optim. Theory Appl. 154 (2012) 217–234] and extends the convergence properties for the class of φ-divergence distances and Bregman distances.

Approximating maps and exact C*-algebras

1982 ◽  
Vol 91 (2) ◽  
pp. 285-289 ◽  
Author(s):  
R. J. Archbold
Keyword(s):  
Tensor Product ◽  
Linear Mapping ◽  
Extra Condition ◽  
Bounded Linear ◽  
C Algebras ◽  
The Right

Let A and E be C*-algebras, let A ⊗ B denote the minimal C*-tensor product, and let ε A *. The right slice map R: A ⊗ B → B is the unique bounded linear mapping with the property that R (a ⊗ b) = (a)b (a ε A, b ε B)(10). A triple (A, B, D), where D is a C*-subalgebra of B, is said to have the slice map property if whenever x ε A ⊗ B and R(x) D for all ε A* then x ε A ⊗ D). It is known that (A, B, D) has the slice map property whenever A is nuclear (11,13), but it appears to be still unknown whether the nuclearity of B will suffice (unless some extra condition is placed on D (l)).

scholarly journals About the number of τ-numbers relative to polynomials with integer coefficients

2021 ◽  
Vol 25 (1) ◽  
pp. 107-117
Author(s):  
Mart Abel ◽  
Helena Lauer ◽  
Ellen Redi
Keyword(s):  
Extra Condition ◽  
Integer Coefficients ◽  
Positive Integers

We show that for all polynomials Q(x) with integer coefficients, that satisfy the extra condition |Q(0) · Q(1) | ≠ 1, there are infinitely many positive integers n such that n is a τ-number relative to the polynomial Q(x). We also find some examples of polynomials Q(x) for which 1 is the only τ-number relative to the polynomial Q(x) and some examples of polynomials Q(x) with |Q(0) · Q(1)|= 1, which have infinitely many positive integers n such that n is a τ-number relative to the polynomial Q(x). In addition, we prove one result about the generators of a τ-number.

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