58 research outputs found
Generalized ulam-hyers stability of C*-Ternary algebra n-Homomorphisms for a functional equation
Fixed points and quadratic equations connected with homomorphisms and derivations on non-Archimedean algebras
The effect of tight glycaemic control, during and after cardiac surgery, on patient mortality and morbidity: A systematic review and meta-analysis
The effects of long-term total parenteral nutrition on gut mucosal immunity in children with short bowel syndrome: a systematic review
BACKGROUND: Short bowel syndrome (SBS) is defined as the malabsorptive state that often follows massive resection of the small intestine. Most cases originate in the newborn period and result from congenital anomalies. It is associated with a high morbidity, is potentially lethal and often requires months, sometimes years, in the hospital and home on total parenteral nutrition (TPN). Long-term survival without parenteral nutrition depends upon establishing enteral nutrition and the process of intestinal adaptation through which the remaining small bowel gradually increases its absorptive capacity. The purpose of this article is to perform a descriptive systematic review of the published articles on the effects of TPN on the intestinal immune system investigating whether long-term TPN induces bacterial translocation, decreases secretory immunoglobulin A (S-IgA), impairs intestinal immunity, and changes mucosal architecture in children with SBS. METHODS: The databases of OVID, such as MEDLINE and CINAHL, Cochran Library, and Evidence-Based Medicine were searched for articles published from 1990 to 2001. Search terms were total parenteral nutrition, children, bacterial translocation, small bowel syndrome, short gut syndrome, intestinal immunity, gut permeability, sepsis, hyperglycemia, immunonutrition, glutamine, enteral tube feeding, and systematic reviews. The goal was to include all clinical studies conducted in children directly addressing the effects of TPN on gut immunity. RESULTS: A total of 13 studies were identified. These 13 studies included a total of 414 infants and children between the ages approximately 4 months to 17 years old, and 16 healthy adults as controls; and they varied in design and were conducted in several disciplines. The results were integrated into common themes. Five themes were identified: 1) sepsis, 2) impaired immune functions: In vitro studies, 3) mortality, 4) villous atrophy, 5) duration of dependency on TPN after bowel resection. CONCLUSION: Based on this exhaustive literature review, there is no direct evidence suggesting that TPN promotes bacterial overgrowth, impairs neutrophil functions, inhibits blood's bactericidal effect, causes villous atrophy, or causes to death in human model. The hypothesis relating negative effects of TPN on gut immunity remains attractive, but unproven. Enteral nutrition is cheaper, but no safer than TPN. Based on the current evidence, TPN seems to be safe and a life saving solution
Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings
In 1940 S. M. Ulam proposed at the University of Wisconsin the problem:
“Give conditions in order for a linear mapping near an approximately
linear mapping to exist.” In 1968 S. U. Ulam proposed the more
general problem: “When is it true that by changing a little the
hypotheses of a theorem one can still assert that the thesis of the
theorem remains true or approximately true?” In 1978 P. M. Gruber
proposed the Ulam type problem: “Suppose a mathematical object
satisfies a certain property approximately. Is it then possible to
approximate this object by objects, satisfying the property exactly?”
According to P. M. Gruber this kind of stability problems is of
particular interest in probability theory and in the case of functional
equations of different types. In 1982-1996 we solved the above Ulam
problem, or equivalently the Ulam type problem for linear mappings and
established analogous stability problems. In this paper we first
introduce new quadratic weighted means and fundamental functional
equations and then solve the Ulam stability problem for non-linear
Euler-Lagrange quadratic mappings Q: X –> Y, satisfying a mean equation
and functional equation
m(1)m(2)Q(a(1)x(1) + a(2)x(2)) + Q(m(2)a(2)x(1) - m(1)a(1)x(2))
= (m(1)a(1)(2) + m(2)a(2)(2))[m(2)Q(x(1)) + m(1)Q(x(2))]
for all 2-dimensional vectors (x(1), x(2)) is an element of X-2, with X
a normed linear space (Y = a real complete normed linear space), and any
fixed pair (a(1), a(2)) of reals ai and any fixed pair (m(1), m(2)) of
positive reals m(i) (i = 1, 2),
0 < m = m(1) + m(2)/m(1)m(2) + 1 (m(1)a(1)(2) + m(2)a(2)(2)). + m2
(C) 1998 Academic Press
Landau's type inequalities
{Let X be a complex Banach space, and let t --> T(t)
(\textbackslash{}\textbackslash{}T(t)\textbackslash{}\textbackslash{}
less than or equal to 1, t greater than or equal to 0) be a strongly
continuous contraction semigroup (on X) with infinitesimal generator A.
This paper proves that
\textbackslash{}\textbackslash{}Ax\textbackslash{}\textbackslash{}(4)
less than or equal to
1024/3\textbackslash{}\textbackslash{}x\textbackslash{}\textbackslash{}(
3)\textbackslash{}\textbackslash{}A(4)x\textbackslash{}\textbackslash{},
\textbackslash{}\textbackslash{}A(2)x\textbackslash{}\textbackslash{}(4)
less than or equal to
10(4)/9\textbackslash{}\textbackslash{}x\textbackslash{}\textbackslash{}
(2)\textbackslash{}\textbackslash{}A(4)x\textbackslash{}\textbackslash{}
(2),
\textbackslash{}\textbackslash{}A(3)x\textbackslash{}\textbackslash{}(4)
less than or equal to
192\textbackslash{}\textbackslash{}x\textbackslash{}\textbackslash{}\tex
tbackslash{}\textbackslash{}A(4)x\textbackslash{}\textbackslash{}(3)
hold for every x is an element of D(A(4)). Inequalities are established
also for uniformly bounded strongly continuous semigroups, groups, and
cosine functions. (C) 1996 Academic Press, Inc.
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