83 research outputs found
Mackey-Glass type delay differential equations near the boundary of absolute stability
For equations with -nonlinearity which has negative Schwarzian derivative and
satisfies for , we prove convergence of all solutions to
zero when both and are less than some constant
(independent on ). This result gives additional insight to the
conjecture about the equivalence between local and global asymptotical
stabilities in the Mackey-Glass type delay differential equations.Comment: 16 pages, 1 figure, accepted for publication in the Journal of
Mathematical Analysis and Application
Global stability in a regulated logistic growth model
Trofimchuk, S. Instituto de MatemΓ‘tica y FΓsica, Universidad de Talca, Casilla 747, Talca, Chile.We investigate global stability of the regulated logistic growth model (RLC) n'(t) = rn(t)(1-n(t-h)/K-cu(t)), u'(t) = -au(t)+bn(t-h). It was proposed by Gopalsamy and Weng [1, 2] and studied recently in [4, 5, 6, 9]. Compared with the previous results, our stability condition is of different kind and has the asymptotical form. Namely, we prove that for the fixed parameters K and mu = bcK/a (which determine the levels of steady states in the delayed logistic equation n'(t) rn(t)(1 - n(t - h)/K) and in RLG) and for every hr < root 2 the regulated logistic growth model is globally stable if we take the dissipation parameter a sufficiently large. On the other hand, studying the local stability of the positive steady state, we observe the improvement of stability for the small values of a: in this case, the inequality rh < pi(1 + mu)/2 guaranties such a stabilit
Yorke and Wright 3/2-stability theorems from a unified point of view
We consider a family of scalar delay differential equations ,
with a nonlinearity satisfying a negative feedback condition combined with
a boundedness condition. We present a global stability criterion for this
family, which in particular unifies the celebrated 3/2-conditions given for the
Yorke and the Wright type equations. We illustrate our results with some
applications.Comment: 10 pages, accepted for publication in the Expanded Volume of DCDS,
devoted to the fourth international conference on Dynamical Systems and
Differential Equations, held at UNC at Wilmington, May 2002. Minor changes
from the previous versio
Pushed traveling fronts in monostable equations with monotone delayed reaction
We study the existence and uniqueness of wavefronts to the scalar
reaction-diffusion equations with monotone delayed reaction term and . We are mostly interested in the situation when the graph of is not
dominated by its tangent line at zero, i.e. when the condition , is not satisfied. It is well known that, in such a case, a
special type of rapidly decreasing wavefronts (pushed fronts) can appear in
non-delayed equations (i.e. with ). One of our main goals here is to
establish a similar result for . We prove the existence of the minimal
speed of propagation, the uniqueness of wavefronts (up to a translation) and
describe their asymptotics at . We also present a new uniqueness
result for a class of nonlocal lattice equations.Comment: 17 pages, submitte
The influence of diverse optical wavelengths on growth rate of Chlorella Vulgaris microalgae
The effect of different optical wavelengths on growth and development of microalgae had been examined repeatedly. Many articles had been published over the subject, although the results of these investigations were frequently controversial. Depending on the number of days spent on cultivation process, yield gain could be both significant and barely noticeable. Also, irradiation intensity plays vital part in microalgae functioning
The influence of PAR irradiance on yield growth of Chlorella microalgae
The experiment indicated the influence of different PAR irradiance conditions on biomass growth of Chlorella vulgaris Beijer stock culture. The absorption spectrum of suspension was evaluated with spectrophotometer SF-256 UVI LOMO Photonika. In this work, effects of LED lamps with various radiant powers on yield gain were compared by analyzing the relation between cells concentration increase and time. It was concluded, that light is the most important factor influencing growth and cells development, as well as nutrient solution, temperature and carbon dioxide provision
ΠΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π³ΡΠΈΠΏΠΏΠ°, Π²ΡΠ·Π²Π°Π½Π½ΠΎΠ³ΠΎ Π½ΠΎΠ²ΡΠΌ Π²ΠΈΡΡΡΠΎΠΌ Π / H1N1 / CA / 2009, Ρ Π±ΠΎΠ»ΡΠ½ΡΡ Π² Π°ΠΌΠ±ΡΠ»Π°ΡΠΎΡΠ½ΠΎΠΉ ΠΏΡΠ°ΠΊΡΠΈΠΊΠ΅
Summary. Emergence of a new influenza virus Π / H1N1 / CA / 2009 (IA2009) in OctoberβDecember, 2009, in Russia required to investigate clinical features of the infection and effectiveness of treatment in ambulatory practice. Information from outpatient medical cards of 44 patients seeking for medical aid because of acute respiratory viral infection (ARVI) during pandemic 2009 was analyzed. All patients were examined for the presence of influenza Π / H1N1 / CA / 2009 virus RNA, seasonal influenza virus RNA and influenza B virus RNA in nasopharyngeal swabs using polymerase chain reaction (PCR). According to the PCR results, patients were identified as having influenza Π / H1N1 (n = 21) or other ARVI (n = 23). Signs and symptoms, complete blood count test, urine test, and chest X-ray were analyzed. Retrospective analysis found that 76.2 % of influenza Π / H1N1 patients had acute respiratory diseases during previous 12 months and 19.0 % of them were healthcare workers. Leading symptoms and signs in patients with influenza Π / H1N1 were cough, headache, weakness, myalgia, fever, obstruction of upper and lower airways. Mild course of disease was observed only in 23.8 % of the cases with recovery during 10 days. Complications were found in 28.6 % of the patients, 14.3 % of them were hospitalized. The most frequent changes in complete blood count tests were accelerated erythrocyte sedimentation rate, neutropenia / leucopenia, lymphocytosis, monocytosis, anisocytosis, thrombocyte aggregation. In 31.3 % cases, changes in white cell count remained after clinical recovery and resolving all respiratory symptoms. Administration of antiviral antibiotic Ingavirin in patients with influenza Π / H1N1 started in the first 2 days of the disease was more effective compared with immunomodulating drug Arbidol.Π Π΅Π·ΡΠΌΠ΅. ΠΠΏΠΈΠ΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠΈΡΠΊΡΠ»ΡΡΠΈΡ Π½ΠΎΠ²ΠΎΠ³ΠΎ Π²ΠΈΡΡΡΠ° Π³ΡΠΈΠΏΠΏΠ° Π / H1N1 / CA / 2009 Π² Π ΠΎΡΡΠΈΠΈ Π² ΠΎΠΊΡΡΠ±ΡΠ΅βΠ΄Π΅ΠΊΠ°Π±ΡΠ΅ 2009 Π³. ΠΏΠΎΡΡΠ΅Π±ΠΎΠ²Π°Π»Π° ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π±ΠΎΠ»Π΅Π·Π½ΠΈ ΠΈ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Π»Π΅ΡΠ΅Π½ΠΈΡ Π±ΠΎΠ»ΡΠ½ΡΡ
Π³ΡΠΈΠΏΠΏΠΎΠΌ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΠΏΠΎΠ»ΠΈΠΊΠ»ΠΈΠ½ΠΈΠΊΠΈ. ΠΡΠ» ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ Π°Π½Π°Π»ΠΈΠ· Π΄Π°Π½Π½ΡΡ
44 Π°ΠΌΠ±ΡΠ»Π°ΡΠΎΡΠ½ΡΡ
ΠΊΠ°ΡΡ Π±ΠΎΠ»ΡΠ½ΡΡ
, ΠΎΠ±ΡΠ°ΡΠΈΠ²ΡΠΈΡ
ΡΡ Π² ΠΏΠΎΠ»ΠΈΠΊΠ»ΠΈΠ½ΠΈΠΊΡ Π² ΠΏΠ΅ΡΠΈΠΎΠ΄ ΡΠΏΠΈΠ΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠΎΠ΄ΡΠ΅ΠΌΠ° Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π΅ΠΌΠΎΡΡΠΈ ΠΏΠΎ ΠΏΠΎΠ²ΠΎΠ΄Ρ ΠΎΡΡΡΠΎΠΉ ΡΠ΅ΡΠΏΠΈΡΠ°ΡΠΎΡΠ½ΠΎΠΉ Π²ΠΈΡΡΡΠ½ΠΎΠΉ ΠΈΠ½ΡΠ΅ΠΊΡΠΈΠΈ. ΠΡΠ΅ Π±ΠΎΠ»ΡΠ½ΡΠ΅ Π±ΡΠ»ΠΈ ΠΎΠ±ΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Ρ Π½Π° Π½Π°Π»ΠΈΡΠΈΠ΅ Π ΠΠ Π²ΠΈΡΡΡΠ° Π³ΡΠΈΠΏΠΏΠ° Π / H1N1 / CA / 2009, ΡΠ΅Π·ΠΎΠ½Π½ΠΎΠ³ΠΎ Π³ΡΠΈΠΏΠΏΠ° Π ΠΈ Π³ΡΠΈΠΏΠΏΠ° Π Π² ΠΌΠ°Π·ΠΊΠ°Ρ
ΡΠΎ ΡΠ»ΠΈΠ·ΠΈΡΡΠΎΠΉ Π½ΠΎΡΠΎΠ³Π»ΠΎΡΠΊΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΏΠΎΠ»ΠΈΠΌΠ΅ΡΠ°Π·Π½ΠΎΠΉ ΡΠ΅ΠΏΠ½ΠΎΠΉ ΡΠ΅Π°ΠΊΡΠΈΠΈ (ΠΠ¦Π ) Π² ΡΠ΅ΠΆΠΈΠΌΠ΅ ΡΠ΅Π°Π»ΡΠ½ΠΎΠ³ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ. ΠΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΠ¦Π Π±ΡΠ»ΠΈ Π²ΡΠ΄Π΅Π»Π΅Π½Ρ Π±ΠΎΠ»ΡΠ½ΡΠ΅ Π³ΡΠΈΠΏΠΏΠΎΠΌ Π / H1N1 (n = 21) ΠΈ ΠΠ ΠΠ (n = 23). ΠΠ½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π»ΠΈΡΡ ΡΠ°ΡΡΠΎΡΠ° ΡΡΠ±ΡΠ΅ΠΊΡΠΈΠ²Π½ΡΡ
ΠΈ ΠΎΠ±ΡΠ΅ΠΊΡΠΈΠ²Π½ΡΡ
ΠΏΡΠΈΠ·Π½Π°ΠΊΠΎΠ² Π±ΠΎΠ»Π΅Π·Π½ΠΈ, ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΠΈ Π°Π½Π°Π»ΠΈΠ·Π° ΠΊΡΠΎΠ²ΠΈ, ΠΎΠ±ΡΠ΅Π³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° ΠΌΠΎΡΠΈ, ΡΠ΅Π½ΡΠ³Π΅Π½ΠΎΠ³ΡΠ°ΡΠΈΠΈ Π³ΡΡΠ΄Π½ΠΎΠΉ ΠΊΠ»Π΅ΡΠΊΠΈ, ΡΠ°ΠΊΡΠΈΠΊΠ° Π²Π΅Π΄Π΅Π½ΠΈΡ Π±ΠΎΠ»ΡΠ½ΡΡ
. ΠΡΠ΅Π½ΠΈΠ²Π°Π»ΠΈΡΡ ΡΡΠΆΠ΅ΡΡΡ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΈ ΡΠ°ΡΡΠΎΡΠ° ΠΎΡΠ»ΠΎΠΆΠ½Π΅Π½ΠΈΠΉ, Π΄Π°Π½Π½ΡΠ΅ ΠΎΠ± ΠΎΡΡΡΡΡ
Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π½ΠΈΡΡ
Π² ΠΏΠΎΡΠ»Π΅Π΄Π½ΠΈΠ΅ 12 ΠΌΠ΅Ρ., Π° ΡΠ°ΠΊ ΠΆΠ΅ Ρ
ΡΠΎΠ½ΠΈΡΠ΅ΡΠΊΠΈΡ
Π±ΠΎΠ»Π΅Π·Π½ΡΡ
. Π Π΅ΡΡΠΎΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΡΠΉ Π°Π½Π°Π»ΠΈΠ· Π΄Π°Π½Π½ΡΡ
Π°ΠΌΠ±ΡΠ»Π°ΡΠΎΡΠ½ΡΡ
ΠΊΠ°ΡΡ ΠΏΠΎΠΊΠ°Π·Π°Π», ΡΡΠΎ 76,2 % Π±ΠΎΠ»ΡΠ½ΡΡ
Π³ΡΠΈΠΏΠΏΠΎΠΌ Π² ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ 12 ΠΌΠ΅Ρ. Π΄ΠΎ ΡΠΏΠΈΠ΄Π΅ΠΌΠΈΠΈ ΠΏΠ΅ΡΠ΅Π½Π΅ΡΠ»ΠΈ ΠΎΡΡΡΠΎΠ΅ Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π½ΠΈΠ΅ ΠΎΡΠ³Π°Π½ΠΎΠ² Π΄ΡΡ
Π°Π½ΠΈΡ. 19 % Π±ΠΎΠ»ΡΠ½ΡΡ
Π³ΡΠΈΠΏΠΏΠΎΠΌ Π±ΡΠ»ΠΈ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌΠΈ ΡΠ°Π±ΠΎΡΠ½ΠΈΠΊΠ°ΠΌΠΈ. Π ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ 3 Π΄Π½Π΅ΠΉ ΠΎΡ Π½Π°ΡΠ°Π»Π° Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π½ΠΈΡ ΠΎΠ±ΡΠ°ΡΠΈΠ»ΠΈΡΡ Π·Π° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΎΠΉ ΠΏΠΎΠΌΠΎΡΡΡ 14,3 % ΠΏΠ°ΡΠΈΠ΅Π½ΡΠΎΠ²; Π²Π΅Π΄ΡΡΠΈΠΌΠΈ ΡΡΠ±ΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠΌΠΈ ΡΠΈΠΌΠΏΡΠΎΠΌΠ°ΠΌΠΈ Π±ΡΠ»ΠΈ ΠΊΠ°ΡΠ΅Π»Ρ, Π³ΠΎΠ»ΠΎΠ²Π½Π°Ρ Π±ΠΎΠ»Ρ, ΡΠ»Π°Π±ΠΎΡΡΡ, Π±ΠΎΠ»Ρ Π² ΠΌΡΡΡΠ°Ρ
. Π ΠΊΠ»ΠΈΠ½ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΊΠ°ΡΡΠΈΠ½Π΅ Π΄Π»Ρ Π³ΡΠΈΠΏΠΏΠ° Π±ΡΠ»ΠΈ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ½Ρ ΠΏΠΎΠ²ΡΡΠ΅Π½Π½Π°Ρ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ° (100 % ΡΠ»ΡΡΠ°Π΅Π²), ΠΏΠΎΡΠ°ΠΆΠ΅Π½ΠΈΠ΅ Π²Π΅ΡΡ
Π½ΠΈΡ
ΠΈ Π½ΠΈΠΆΠ½ΠΈΡ
ΠΎΡΠ΄Π΅Π»ΠΎΠ² Π΄ΡΡ
Π°ΡΠ΅Π»ΡΠ½ΡΡ
ΠΏΡΡΠ΅ΠΉ Ρ ΠΏΡΠΈΠ·Π½Π°ΠΊΠ°ΠΌΠΈ ΠΎΠ±ΡΡΡΡΠΊΡΠΈΠΈ. Π 76,2 % ΡΠ»ΡΡΠ°Π΅Π² ΠΎΡΠΌΠ΅ΡΠ°Π»ΠΎΡΡ ΡΡΠ΅Π΄Π½Π΅ΡΡΠΆΠ΅Π»ΠΎΠ΅ ΠΈ ΡΡΠΆΠ΅Π»ΠΎΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ Π±ΠΎΠ»Π΅Π·Π½ΠΈ. ΠΡΠ»ΠΎΠΆΠ½Π΅Π½ΠΈΡ ΠΈΠΌΠ΅Π»ΠΈ 28,6 % ΠΏΠ°ΡΠΈΠ΅Π½ΡΠΎΠ², Π² 14,3 % ΡΠ»ΡΡΠ°Π΅Π² ΠΈΠΌ Π±ΡΠ»Π° Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠ° Π³ΠΎΡΠΏΠΈΡΠ°Π»ΠΈΠ·Π°ΡΠΈΡ. ΠΠΈΡΡΡ Π³ΡΠΈΠΏΠΏΠ° ΠΎΠ±Π½Π°ΡΡΠΆΠΈΠ²Π°Π»ΡΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΠ¦Π Π² ΡΠ»ΠΈΠ·ΠΈ ΠΈΠ· Π½ΠΎΡΠΎΠ³Π»ΠΎΡΠΊΠΈ Π΄ΠΎ 11 Π΄Π½Π΅ΠΉ Π±ΠΎΠ»Π΅Π·Π½ΠΈ. ΠΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ Π² Π°Π½Π°Π»ΠΈΠ·Π΅ ΠΊΡΠΎΠ²ΠΈ ΠΏΡΠΈ Π³ΡΠΈΠΏΠΏΠ΅ Π±ΡΠ»ΠΈ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½Ρ Π² 100 % ΡΠ»ΡΡΠ°Π΅Π². ΠΠ°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΠ°ΡΡΡΠΌΠΈ Π±ΡΠ»ΠΈ ΡΡΠΊΠΎΡΠ΅Π½ΠΈΠ΅ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΎΡΠ΅Π΄Π°Π½ΠΈΡ ΡΡΠΈΡΡΠΎΡΠΈΡΠΎΠ², Π½Π΅ΠΉΡΡΠΎΠΏΠ΅Π½ΠΈΡ / Π»Π΅ΠΉΠΊΠΎΠΏΠ΅Π½ΠΈΡ, Π»ΠΈΠΌΡΠΎΡΠΈΡΠΎΠ·, ΠΌΠΎΠ½ΠΎΡΠΈΡΠΎΠ·, Π°Π½ΠΈΠ·ΠΎΡΠΈΡΠΎΠ·, Π°Π³ΡΠ΅Π³Π°ΡΠΈΡ ΡΡΠΎΠΌΠ±ΠΎΡΠΈΡΠΎΠ², ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠΎΡ
ΡΠ°Π½ΡΠ»ΠΈΡΡ Π² 31,3 % ΡΠ»ΡΡΠ°Π΅Π² ΠΈ ΠΏΡΠΈ ΠΎΡΡΡΡΡΡΠ²ΠΈΠΈ ΠΊΠ»ΠΈΠ½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΈΠΌΠΏΡΠΎΠΌΠΎΠ². ΠΡΠΎΡΠΈΠ²ΠΎΠ²ΠΈΡΡΡΠ½Π°Ρ ΡΠ΅ΡΠ°ΠΏΠΈΡ Π² ΠΏΠ΅ΡΠ²ΡΠ΅ 2 ΡΡΡ. ΠΎΡ Π½Π°ΡΠ°Π»Π° Π³ΡΠΈΠΏΠΏΠ° ΠΈ ΠΠ ΠΠ ΡΠΎΠΊΡΠ°ΡΠ°Π»Π° ΠΏΡΠΎΠ΄ΠΎΠ»ΠΆΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΡ Π±ΠΎΠ»Π΅Π·Π½ΠΈ. ΠΠ°Π·Π½Π°ΡΠ΅Π½ΠΈΠ΅ ΠΏΡΠ΅ΠΏΠ°ΡΠ°ΡΠ° ΠΈΠ½Π³Π°Π²ΠΈΡΠΈΠ½ ΠΏΡΠΈ Π³ΡΠΈΠΏΠΏΠ΅ Π±ΡΠ»ΠΎ Π±ΠΎΠ»Π΅Π΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎ, ΡΠ΅ΠΌ ΠΏΡΠ΅ΠΏΠ°ΡΠ°ΡΠ° Π°ΡΠ±ΠΈΠ΄ΠΎΠ»
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