scholarly journals Superstability of the generalized orthogonality equation on restricted domains

2004 ◽  
Vol 114 (3) ◽  
pp. 253-267 ◽  
Author(s):  
Soon-Mo Jung ◽  
Prasanna K. Sahoo
Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 282
Author(s):  
Ginkyu Choi ◽  
Soon-Mo Jung

We will prove the generalized Hyers–Ulam stability of isometries, with a focus on the stability for restricted domains. More precisely, we prove the generalized Hyers–Ulam stability of the orthogonality equation and we use this result to prove the stability of the equations ∥f(x)−f(y)∥=∥x−y∥ and ∥f(x)−f(y)∥2=∥x−y∥2 on the restricted domains. As we can easily see, these functional equations are symmetric in the sense that they become the same equations even if the roles of variables x and y are exchanged.


Development ◽  
1988 ◽  
Vol 104 (2) ◽  
pp. 305-316 ◽  
Author(s):  
D. Davidson ◽  
E. Graham ◽  
C. Sime ◽  
R. Hill

The mouse genes En-1 and En-2 display sequence similarity, in and around the homeobox region, to the engrailed family in Drosophila. This paper describes their pattern of expression in the 12.5-day mouse embryo as determined by in situ hybridization. En-2 is expressed in a subset of cells expressing En-1. Both genes are expressed in the developing midbrain and its junction with the hindbrain. In addition, En-1 is expressed in the floor of the hindbrain, a restricted ventrolateral segment of the neural tube throughout the trunk and anterior part of the tail, the dermatome of tail somites, the centrum and costal processes in developing vertebrae, a restricted region of facial mesenchyme and the limb-bud ectoderm. Supplementary studies of 9.5-day and 10.5-day embryos showed that the same pattern of expression pertained in the neural tube, but that expression in the somites is at first confined to the dermatome and later found at a low level in restricted sclerotomal regions. Both genes are expressed in restricted domains which do not cross tissue-type boundaries. In several instances, however, boundaries of expression lie within morphologically undifferentiated tissue. These results suggest that En-1 and En-2 may be involved in the establishment or maintenance of the spatial integrity of specific domains within developing tissues.


2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Margherita Fochi

Based on the studies on the Hyers-Ulam stability and the orthogonal stability of some Pexider-quadratic functional equations, in this paper we find the general solutions of two quadratic functional equations of Pexider type. Both equations are studied in restricted domains: the first equation is studied on the restricted domain of the orthogonal vectors in the sense of Rätz, and the second equation is considered on the orthogonal vectors in the inner product spaces with the usual orthogonality.


2016 ◽  
Vol 30 (1) ◽  
pp. 93-116 ◽  
Author(s):  
Robert Sparrow

There is increasing speculation within military and policy circles that the future of armed conflict is likely to include extensive deployment of robots designed to identify targets and destroy them without the direct oversight of a human operator. My aim in this paper is twofold. First, I will argue that the ethical case for allowing autonomous targeting, at least in specific restricted domains, is stronger than critics have typically acknowledged. Second, I will attempt to defend the intuition that, even so, there is something ethically problematic about such targeting. I argue that an account of the nonconsequentialist foundations of the principle of distinction suggests that the use of autonomous weapon systems (AWS) is unethical by virtue of failing to show appropriate respect for the humanity of our enemies. However, the success of the strongest form of this argument depends upon understanding the robot itself as doing the killing. To the extent that we believe that, on the contrary, AWS are only a means used by combatants to kill, the idea that the use of AWS fails to respect the humanity of our enemy will turn upon an account of what is required by respect, which is essential conventional. Thus, while the theoretical foundations of the idea that AWS are weapons that are “evil in themselves” are weaker than critics have sometimes maintained, they are nonetheless sufficient to demand a prohibition of the development and deployment of such weapons.


2021 ◽  
Vol 3 (3) ◽  
pp. 290-315
Author(s):  
Esther Olayinka Bamigbola ◽  
Fadekemi Rukayat Umar

This study investigates the factors that are responsible for the levelling of Ìkàr??-Àkókó dialect. Specifically, the paper examines the impacts of Nigerian indigenous languages, especially Yorùbá, on the dialect. The study aims at identifying the patterns of changes in the dialect and their impacts on the ethnic identities of the people. The work is based on the variationist approach pioneered by William Labov in the late 1960s and early 1970s. The tools used for data collection include questionnaire, oral interview and observation. The findings of the study reveal that the dialect manifests different stages of changes, vital domains like home, school and work place, which are supposed to be the strongholds of this dialect are being encroached upon by languages other than the mother tongue in the study area. It was found that the changes in the dialect are not due to the influence of English language only, but to indigenous Nigerian languages, mostly Yorùbá. It was concluded that the gradual levelling of Ìkàr??-Àkókó dialect is caused in part by restricted domains of use, increase in population; lack of commitment to indigenous language use by the native speakers; and suppressive language policy in the nation. The study recommends sensitization campaigns as a way of maintaining and sustaining the status of indigenous languages.


Development ◽  
2000 ◽  
Vol 127 (17) ◽  
pp. 3789-3794 ◽  
Author(s):  
R. Huang ◽  
Q. Zhi ◽  
K. Patel ◽  
J. Wilting ◽  
B. Christ

Bones of the postcranial skeleton of higher vertebrates originate from either somitic mesoderm or somatopleural layer of the lateral plate mesoderm. Controversy surrounds the origin of the scapula, a major component of the shoulder girdle, with both somitic and lateral plate origins being proposed. Abnormal scapular development has been described in the naturally occurring undulated series of mouse mutants, which has implicated Pax1 in the formation of this bone. Here we addressed the development of the scapula, firstly, by analysing the relationship between Pax1 expression and chondrogenesis and, secondly, by determining the developmental origin of the scapula using chick quail chimeric analysis. We show the following. (1) The scapula develops in a rostral-to-caudal direction and overt chondrification is preceded by an accumulation of Pax1-expressing cells. (2) The scapular head and neck are of lateral plate mesodermal origin. (3) In contrast, the scapular blade is composed of somitic cells. (4) Unlike the Pax1-positive cells of the vertebral column, which are of sclerotomal origin, the Pax1-positive cells of the scapular blade originate from the dermomyotome. (5) Finally, we show that cells of the scapular blade are organised into spatially restricted domains along its rostrocaudal axis in the same order as the somites from which they originated. Our results imply that the scapular blade is an ossifying muscular insertion rather than an original skeletal element, and that the scapular head and neck are homologous to the ‘true coracoid’ of higher vertebrates.


Development ◽  
1996 ◽  
Vol 122 (5) ◽  
pp. 1395-1407 ◽  
Author(s):  
C. Samakovlis ◽  
N. Hacohen ◽  
G. Manning ◽  
D.C. Sutherland ◽  
K. Guillemin ◽  
...  

The tracheal (respiratory) system of Drosophila melanogaster is a branched network of epithelial tubes that ramifies throughout the body and transports oxygen to the tissues. It forms by a series of sequential branching events in each hemisegment from T2 to A8. Here we present a cellular and initial genetic analysis of the branching process. We show that although branching is sequential it is not iterative. The three levels of branching that we distinguish involve different cellular mechanisms of tube formation. Primary branches are multicellular tubes that arise by cell migration and intercalation; secondary branches are unicellular tubes formed by individual tracheal cells; terminal branches are subcellular tubes formed within long cytoplasmic extensions. Each level of branching is accompanied by expression of a different set of enhancer trap markers. These sets of markers are sequentially activated in progressively restricted domains and ultimately individual tracheal cells that are actively forming new branches. A clonal analysis demonstrates that branching fates are not assigned to tracheal cells until after cell division ceases and branching begins. We further show that the breathless FGF receptor, a tracheal gene required for primary branching, is also required to activate expression of markers involved in secondary branching and that the pointed ETS-domain transcription factor is required for secondary branching and also to activate expression of terminal branch markers. The combined morphological, marker expression and genetic data support a model in which successive branching events are mechanistically and genetically distinct but coupled through the action of a tracheal gene regulatory hierarchy.


Sign in / Sign up

Export Citation Format

Share Document