The Perron Problem for C-Semigroups

&lt;p&gt;Characterizations of Perron-type for the exponential stability of exponentially bounded C-semigroups are given. Also, some applications for the asymptotic behavior of the integrated semigroups are obtained.&lt;/p&gt;</p

A STOCHASTIC MODELING FOR THE UNSTABLE FINANCIAL MARKETS

Considering the present economic context, the measurement of performances has become a permanent preoccupation for organizations, since the whole process is based on it, offering the necessary feedback to identify both the positive actions which have led to favorable results for the organization, and the negative ones, in order to correct them in the future. To do this, we have to measure what is most importantly to measure. Starting from these considerations, the present paper approaches from a theoretical and practical point of view the economic rate of return as the indicator which synthesizes best an organization’s financial-economic performance. We have calculated and analyzed the economic rate of return for a group of Ten Romanian Firms in the food industry, through different calculation relations, pointing out the advantages/disadvantages of each calculation method.belated integral, forward-backward stochastic equations, pathwise uniqueness, financial modeling.

Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations

We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates a C0-semigroup {()}≥0). The novelty of our approach consists in the fact that we do not assume the T(t)-invariance of the unstable manifolds. Roughly speaking, we prove that if the solution of the corresponding inhomogeneous difference equation belongs to any sequence space (on which the right shift is an isometry) for every inhomogeneity from the same class of sequence spaces, then the continuous-time solutions of the autonomous homogeneous differential equation will exhibit a (no past) exponential dichotomic behavior. This approach has many advantages among which we emphasize on the facts that the aforementioned condition is very general (since the class of sequence spaces that we use includes almost all the known sequence spaces, as the classical ℓ spaces, sequence Orlicz spaces, etc.) and that from discrete-time conditions we get information about the continuous-time behavior of the solutions

Case report: Tackling the complexities of an extremely premature newborn with intrauterine growth restriction and congenital metabolic disorders through a multidisciplinary approach

Background and objectivesThe premature birth of a newborn can present a complex challenge for healthcare providers, particularly in cases of extreme prematurity combined with intrauterine growth restriction and multiple metabolic deficiencies. In this report, we aim to shed light on the difficulties and considerations involved in the management of such a case. In addition, our study is aimed to raise awareness of the importance of a multidisciplinary team in managing an extreme premature case with multiple comorbidities.Case presentation and main findingsWe present the case of a 28-week premature female newborn with very low birth weight (660 g, percentile &lt;10%) and intrauterine growth restriction. She was born through emergency cesarean delivery due to maternal Hemolysis, Elevated Liver enzymes, and Low Platelet count (HELLP) syndrome and had a high-risk pregnancy (spontaneous twin pregnancy, with one fetus stopping development at 16 weeks and maternal hypertension). In the first hours of life, she presented with persistent hypoglycemia requiring progressive glucose supplementation up to 16 g/kg/day to maintain normal blood glucose levels. The baby then showed favorable progress. However, from days 24 to 25, hypoglycemia recurred and did not respond to glucose boluses or supplementation in both intravenous and oral feeds, leading to the suspicion of a congenital metabolic disorder. Endocrine and metabolic screenings led to suspicion of primary carnitine deficiency and a deficiency in hepatic form of carnitine-palmitoyltransferase type I (CPT1) on the second screening.Conclusion and clinical implicationsThe study highlights rare metabolic anomalies that can be due to both organ and system immaturity and delayed enteral feeding and excessive use of antibiotics. The clinical implications of this study emphasize the need for careful monitoring and comprehensive care of premature infants to prevent and manage potential metabolic abnormalities by neonatal metabolic screening

Admissibility and Non-Uniform Dichotomy for Differential Systems

The problem of nonuniform exponential dichotomy of linear differential systems in Banach spaces is discussed. It is established a connection between the admissibility of a pair of certain function spaces which are translations invariant, on one hand, and the nonuniform exponential dichotomy of differential systems, on the other. Also, Some results due to Hartman, Massera, Schäffer and Coppel are generalized as well

Some Landau Type Inequalities for Functions whose Derivates are Hölder Continuous

Some inequalities of Landau type for functions whose derivates satisfy Hölder’s condition are pointed out

Lyapunov operator inequalities for exponential stability of Banach space semigroups of operators

AbstractWe obtain continuous-time and discrete-time Lyapunov operator inequalities for the exponential stability of strongly continuous, one-parameter semigroups acting on Banach spaces. Thus we extend the classic result of Datko (1970) [2] from Hilbert spaces to Banach spaces