scholarly journals Errata for “L2-boundedness of the Cauchy transform on smooth non-Lipschitz curves”, Nagoya Math J. 130 (1993), 123–147

1995 ◽  
Vol 137 ◽  
pp. 195-195
Author(s):  
Hyeonbae Kang ◽  
Jinkeun Seo
Keyword(s):  
Symmetry Condition ◽  
Cauchy Transform ◽  
Extra Condition ◽  
Standard Argument ◽  
Nagoya Math

Note that an extra condition of symmetry of f, namely, the boundedness of f(x) = f(− x) is added to the hypothesis of the Lemma. Lemma 2.1 was used in three places in the paper to prove that the functions F, G*, and f given in pages 140, 141, and 144, respectively, belong to BMO. It can be checked by a standard argument that these functions satisfy the symmetry 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 Feasibility of reforms regarding their reaches: An outline of an impossibility theorem

2003 ◽  
Vol 44 (159) ◽  
pp. 7-19
Author(s):  
Ljubomir Madzar
Keyword(s):  
French Revolution ◽  
Initial Position ◽  
Impossibility Theorem ◽  
Reform Process ◽  
Institutional Changes ◽  
Standard Argument ◽  
Lack Of Information ◽  
Run Up ◽  
The One ◽  
The French Revolution

Reform endeavors run up against various sorts of constraints. A major set of constraints is the one derived from the lack of information and knowledge. This category of constraints is inextricably linked with the size of the reform undertakings. The architects of reforms do not have the knowledge needed for designing big institutional changes. Moreover, the big changes take the system far a field from its initial position, the one to be overcome by the reform process. Both features generate two distinct types of uncertainty which are sources of potential hazards and could easily produce the breakdown of the system as a whole with well-known disastrous consequences. This reasoning turns down to the standard argument of feasibility and (there- fore) desirability of the Popper-like piecemeal engineering. Another important issue is the necessity/desirability of preserving old institutions while the new ones are being built lest institutional vacua be developed with disastrous consequences. The argument is analogous to the tenor of the Burke critique of the French Revolution. The upshot of the analysis is that quick implementation of the far-reaching changes is not to be expected and that the going criticisms of the alleged sluggishness of reforms are to some extent ill-advised.

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.

Universal Optimization Efficiency for Nonlinear Irreversible Heat Engines

2017 ◽  
Vol 42 (3) ◽  
Author(s):  
Yanchao Zhang ◽  
Juncheng Guo ◽  
Guoxing Lin ◽  
Jincan Chen
Keyword(s):  
Objective Function ◽  
Strong Coupling ◽  
Power Efficiency ◽  
Symmetry Condition ◽  
Maximum Efficiency ◽  
Cycle Model ◽  
Trade Off ◽  
Heat Engines ◽  
Optimization Efficiency ◽  
Universal Expression

AbstractWe introduce a multi-parameter combined objective function of heat engines under the strong coupling and symmetry condition and derive the universal expression of the optimization efficiency. The results obtained show that the optimization efficiency derived from the multi-parameter combined objective function include a variety of optimization efficiencies, such as the efficiency at the maximum power, efficiency at the maximum efficiency-power state, efficiency at the maximum ecological or unified trade-off function, and Carnot efficiency. It is further explained that these results are also suitable for the endoreversible cycle model of the Carnot heat engines operating between two heat reservoirs.

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