1,835 research outputs found
Boundedness and exponential stability for periodic time dependent systems
The time dependent -periodic system
\begin{equation*}
\dot x{(t)} = A(t)x{(t)} , \ t\in \mathbb{R}, \ \ x(t) \in\mathbb{C}^{n}\tag{A(t)}
\end{equation*}
is uniformly exponentially stable if and only if for each real number and each -periodic, -valued function the solution of the Cauchy Problem
\begin{equation*}
\left\{\begin{split}
\dot y{(t)} &= A(t) y{(t)} + e^{i \mu t}f(t),\ \ t\in \mathbb{R}_+, \ y(t) \in \mathbb{C}^{n} \\
y(0) &= 0
\end{split}\right.
\end{equation*}
is bounded. In this note we prove a result that has the above result as an immediate corollary. Some new characterizations for uniform exponential stability of in terms of the Datko type theorems are also obtained as corollaries
Spectral characterizations for Hyers-Ulam stability
First we prove that an complex linear system is Hyers-Ulam stable if and only if it is dichotomic (i.e. its associated matrix has no eigenvalues on the imaginary axis ). Also we show that the scalar differential equation of order
is Hyers-Ulam stable if and only if the algebraic equation
has no roots on the imaginary axis
Connections between exponential stability and boundedness of solutions of a couple of differential time depending and periodic systems
Among others, we prove that the vectorial time dependent -periodic differential system is uniformly exponentially stable (i.e. all its solutions decay exponentially at infinity) if and only if for each vector , the solution of the Cauchy Problem is bounded on uniformly in respect with the parameter on the entire real axis. As a consequence, we get that the system is uniformly exponentially stable if and only if for each vector the map is bounded on This latter result is a weak version of the Barbashin theorem which seems to be new. Here is the fundamental matrix associated to the system $(A(t)).
Connections between the stability of a Poincare map and boundedness of certain associate sequences
Let and be two natural numbers and let be the -periodic discrete evolution family of matrices, having complex scalars as entries, generated by -valued, -periodic sequence of matrices We prove that the solution of the following discrete problem is bounded for each and each -vector if the Poincare map is stable. The converse statement is also true if we add a new assumption to the boundedness condition. This new assumption refers to the invertibility for each of the matrix By an example it is shown that the assumption on invertibility cannot be removed. Finally, a strong variant of Barbashin's type theorem is proved
Influence of sulphide Cu (I) promoting additives concentration on acid and catalytic properties of high-silica zeolites in straight-run gasoline conversion
In present article the influence of Cu[2]S promoting additives concentration on acid and catalytic properties of high silica MFI-type zeolites is investigated in the process of conversion of straight-run gasoline fractions of gas condensate into high octane components of motor fuels. It was shown that zeolite modified with 1% of Cu[2]S nanoscaled powder possesses the highest acid centers concentration and highest catalytic activity
Switching to Once-Daily Liraglutide From Twice-Daily Exenatide Further Improves Glycemic Control in Patients With Type 2 Diabetes Using Oral Agents
OBJECTIVETo evaluate efficacy and safety of switching from twice-daily exenatide to once-daily liraglutide or of 40 weeks of continuous liraglutide therapy.RESEARCH DESIGN AND METHODSWhen added to oral antidiabetes drugs in a 26-week randomized trial (Liraglutide Effect and Action in Diabetes [LEAD]-6), liraglutide more effectively improved A1C, fasting plasma glucose, and the homeostasis model of β-cell function (HOMA-B) than exenatide, with less persistent nausea and hypoglycemia. In this 14-week extension of LEAD-6, patients switched from 10 μg twice-daily exenatide to 1.8 mg once-daily liraglutide or continued liraglutide.RESULTSSwitching from exenatide to liraglutide further and significantly reduced A1C (0.32%), fasting plasma glucose (0.9 mmol/l), body weight (0.9 kg), and systolic blood pressure (3.8 mmHg) with minimal minor hypoglycemia (1.30 episodes/patient-year) or nausea (3.2%). Among patients continuing liraglutide, further significant decreases in body weight (0.4 kg) and systolic blood pressure (2.2 mmHg) occurred with 0.74 episodes/patient-year of minor hypoglycemia and 1.5% experiencing nausea.CONCLUSIONSConversion from exenatide to liraglutide is well tolerated and provides additional glycemic control and cardiometabolic benefits
Poling effect on distribution of quenched random fields in a uniaxial relaxor ferroelectric
The frequency dependence of the dielectric permitivity's maximum has been
studied for poled and unpoled doped relaxor strontium barium niobate
(SBN-61:Cr). In both cases the maximum
found is broad and the frequency dispersion is strong. The present view of
random fields compensation in the unpoled sample is not suitable for explaining
this experimental result. We propose a new mechanism where the dispersion of
quenched random electric fields, affecting the nanodomains, is minimized after
poling. We test our proposal by numerical simulations on a random field Ising
model. Results obtained are in agreement with the polarization's measurements
presented by Granzow et al. [Phys. Rev. Lett {\bf 92}, 065701 (2004)].Comment: 7 pages, 4 figure
Administration of Endotoxin, Tumor Necrosis Factor, or Interleukin 1 to Rats Activates Skeletal Muscle Branched-Chain α-Keto Acid Dehydrogenase
Protein catabolic states (i.e., sepsis and trauma) are thought to be associated with accelerated oxidation of branched-chain amino acids (BCAA). Branched-chain α-keto acid dehydrogenase (BCKAD), the rate-limiting enzyme for BCAA oxidation by muscle, is regulated by phosphorylation/dephosphorylation. Skeletal muscle BCKAD was only 2-4% active in control rats. Intravenous injection of Salmonella enteritidis endotoxin (0.25-10 mg/kg) did not change total BCKAI) activity, but increased the percent active enzyme in muscle three- to four-fold in 4-6 h. Identical results were observed in adrenalectomized rats pretreated with one dose of α-methylprednisolone (2.5 mg/kg i.p.) 30-60 min before saline or endotoxin injection, indicating that endotoxin\u27s effect was not mediated by hypersecretion of adrenal hormones. Cortisone pretreatment of normal rats (100 mg/kg per d) for 2 d prevented endotoxin-induced activation of muscle BCKAD, suggesting that endogenous secretion products mediated BCKAD activation by endotoxin. Human recombinant tumor necrosis factor-α and/or IL-1β or α (50 μg/kg) increased muscle BCKAD activation two- to fourfold in normal rats 4-6 h after intravenous injection. We conclude that cytokine-mediated activation of muscle BCKAD may contribute to accelerated BCAA oxidation in septicemia
The polaroid image as photo-object
This article is part of a larger project on the cultural history of Polaroid photography and draws on research done at the Polaroid Corporate archive at Harvard and at the Polaroid company itself. It identifies two cultural practices engendered by Polaroid photography, which, at the point of its extinction, has briefly flared into visibility again. It argues that these practices are mistaken as novel but are in fact rediscoveries of practices that stretch back as many as five decades. The first section identifies Polaroid image-making as a photographic equivalent of what Tom Gunning calls the ‘cinema of attractions’. That is, the emphasis in its use is on the display of photographic technologies rather than the resultant image. Equally, the common practice, in both fine art and vernacular circles, of making composite pictures with Polaroid prints, draws attention from image content and redirects it to the photo as object
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