The existence of large convex cones inside the family of real functions whose continuity set is a prescribed subset of a rather general topological space is established in this paper. This ...complements a number of recent assertions concerning lineability that have been obtained by several authors about functions defined on an interval of R. When the prescribed subset is a dense Gδ-set of a topological space satisfying appropriate conditions, an almost reciprocal of the Baire–Kuratowski theorem on 1-Baire functions is obtained, and again the family of functions satisfying the conclusion contains a large convex cone. For a dense Gδ-subset G of R, it is proved the existence of a dense vector subspace with maximal dimension in the space of continuous real functions all of whose nonzero members are derivable and the derivatives are continuous exactly at the points of G. Again, this complements a number of recent results made in the case that G is an open set of R, and yields as a consequence the existence of large vector spaces of 1-Baire functions with prescribed continuity set.
Lineability criteria, with applications Bernal-González, Luis; Ordóñez Cabrera, Manuel
Journal of functional analysis,
03/2014, Letnik:
266, Številka:
6
Journal Article
Recenzirano
Odprti dostop
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, ...additionally, X is endowed with richer structures, then the more stringent notions of dense-lineability, maximal dense-lineability and spaceability arise naturally. In this paper, several lineability criteria are provided and applied to specific topological vector spaces, mainly function spaces. Sometimes, such criteria furnish unified proofs of a number of scattered results in the related literature. Families of strict-order integrable functions, hypercyclic vectors, non-extendable holomorphic mappings, Riemann non-Lebesgue integrable functions, sequences not satisfying the Lebesgue dominated convergence theorem, nowhere analytic functions, bounded variation functions, entire functions with fast growth and Peano curves, among others, are analyzed from the point of view of lineability.
In this paper, we analyze the linear structure of the family
H
e
(
G
) of holomorphic functions on a domain
G
of the complex plane that are not analytically continuable beyond the boundary of
G
. We ...prove that
H
e
(
G
) contains, except for zero, a dense algebra; and, under appropriate conditions, the subfamily of
H
e
(
G
) consisting of boundary-regular functions contains dense vector spaces with maximal dimension as well as infinite dimensional closed vector spaces and large algebras. We also consider the case in which
G
is a domain of existence in a complex Banach space. The results obtained complete or extend a number of previous results by several authors.
Total and non-total suborbits for hypercyclic operators Bernal-González, Luis; Bonilla, Antonio
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas,
2023/1, Letnik:
117, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this note, it is proved that if
X
is a separable infinite dimensional Fréchet space that admits a continuous norm then, given a closed infinite dimensional subspace of
X
, there exists a ...hypercyclic operator admitting a dense orbit which in turn admits a suborbit all of whose sub-suborbits are total in the prescribed subspace. This is related to a recently published result asserting that every supercyclic vector for an operator on a Hilbert space supports a non-total suborbit. Here we also extend this result to normed spaces.
In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is ...shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.
Patients admitted to the intensive care unit (ICU) experience sleep disruption caused by a variety of conditions, such as staff activities, alarms on monitors, and overall noise. In this study, we ...explored the relationship between noise and other factors associated with poor sleep quality in patients.
This was a prospective cohort study. We used the Richards-Campbell Sleep Questionnaire to explore sleep quality in a sample of patients admitted to the ICU of a private hospital. We measured the noise levels within each ICU three times a day. After each night during their ICU stay, patients were asked to complete a survey about sleep disturbances. These disturbances were classified as biological (such as anxiety or pain) and environmental factors (such as lighting and ICU noise).
We interviewed 71 patients; 62% were men (mean age 54.46 years) and the mean length of stay was 8 days. Biological factors affected 36% and environmental factors affected 20% of the patients. The most common biological factor was anxiety symptoms, which affected 28% of the patients, and the most common environmental factor was noise, which affected 32.4%. The overall mean recorded noise level was 62.45 dB. Based on the patients' responses, the environmental factors had a larger effect on patients' sleep quality than biological factors. Patients who stayed more than 5 days reported less sleep disturbance. Patients younger than 55 years were more affected by environmental and biological factors than were those older than 55 years.
Patient quality of sleep in the ICU is associated with environmental factors such as noise and artificial lighting, as well as biological factors related to anxiety and pain. The noise level in the ICU is twice that recommended by international guides. Given the stronger influence of environmental factors, the use of earplugs or sleeping masks is recommended. The longer the hospital stay, the less these factors seem to affect patients' sleep quality.
Celotno besedilo
Dostopno za:
CEKLJ, DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
It is shown in this short note the existence, for each nonzero member of the ideal of D-multiples of convolution operators acting on the space of entire functions, of a scalar multiple of it ...supporting a hypercyclic algebra.
Background: The high incidence of idiopathic scoliosis worldwide as well as the serious health problems it can cause in adulthood, make it necessary to seek effective treatments to prevent the ...progression of the disease to more aggressive treatments such as surgery and improve patients’ quality of life. The use of night braces, besides a less severe influence on the patient’s quality of life, is effective in stopping the progression of the curve in idiopathic scoliosis. Methods: A longitudinal study was performed with an experimental population of 108 participants who attended orthotic treatment at the University Hospital of Barcelona, with ages between 4 and 15 years old, with a main curvature greater than 25 degrees and a Risser between 0 and 3. The participants received treatment with Providence ISJ-3D night braces until their pubertal change (mean duration of 2.78 years for males and 1.97 years for females). Results: The implementation of night-time orthotic treatment in children with idiopathic scoliosis is effective in slowing the progression of the curve and in the prevention of more aggressive treatments such as surgery, maintaining the patient’s quality of life. Conclusions: The use of night braces is efficacious in the treatment of idiopathic scoliosis, although new studies including more sociodemographic data as well as curves from 20 degrees of progression are necessary.
In this note, a vector space of real-analytic functions on the plane is explicitly constructed such that all its nonzero functions are non-integrable but yet their two iterated integrals exist as ...real numbers and coincide. Moreover, it is shown that this vector space is dense in the space of all real continuous functions on the plane endowed with the compact-open topology.
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