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A Boundedness and Stability Results for a Kind of Third Order Delay Differential Equations
Get PDFThe objective of this study was to get some sufficient conditions which guarantee the asymptotic stability and uniform boundedness of the null solution of some differential equations of third order with the variable delay. The most efficient tool for the study of the stability and boundedness of solutions of a given nonlinear differential equation is provided by Lyapunov theory. However the construction of such functions which are positive definite with corresponding negative definite derivatives is in general a difficult task, especially for higher-order differential equations with delay. Such functions and their time derivatives along the system under consideration must satisfy some fundamental inequalities. Here the Lyapunov second method or direct method is used as a basic tool. By defining an appropriate Lyapunov functional, we prove two new theorems on the asymptotic stability and uniform boundedness of the null solution of the considered equation. Our results obtained in this work improve and extend some existing well-known related results in the relevant literature which were obtained for nonlinear differential equations of third order with a constant delay. We also give an example to illustrate the importance of the theoretical analysis in this work and to test the effectiveness of the method employed
1-(1-Propylsulfonic)-3-methylimidazolium chloride acidic ionic liquid catalyzed hydrolysis of cellulose in water: Effect of metal ion co-catalysts
No full textAbstract The effect of eight metal ions, Cr3 +, Mn2 +, Fe3 +, Co2 + Ni2 +, Cu2 +, Zn2 + and La3 + on 1-(1-propylsulfonic)-3-methylimidazolium chloride acidic ionic liquid catalyzed hydrolysis of cellulose in water was studied at 140-170 °C. Mn2 +, Fe3 +, and Co2 + as co-catalysts produced significant enhancements in total reducing sugar (TRS) yields, with Mn2 + showing the highest activity. Mn2 + as co-catalyst produced 91.8, and 91.9% TRS yields, whereas samples without Mn2 + gave 28.0 and 28.7% yields at 160 and 170 °C respectively. The observed activation energies for cellulose hydrolysis without a co-catalyst and with Mn2 + co-catalyst are 78.1 ± 1.4 and 32.8 ± 4.9 kJ·mol- 1 respectively
γ-Valerolactone from pyrolysis of calcium salts of levulinic-formic acid mixtures derived from cellulose
No full textHydrothermal degradation of cellulose (DP~450) in 0.02-0.20moldm-3 aq. hydrochloric acid at 160°C, for 2-8h and neutralization of the filtrate with calcium hydroxide can be used to prepare a mixture of carboxylic acid calcium salts. The mixture consists of calcium levulinate and calcium formate in approximately 1:0.65mol ratio, together with CaCl2. Pyrolysis of this crude mixture at 350°C for 3.0min produces pyrolyzate oil yield of 140-210gkg-1 of dry salt mixture. The pyrolyzate was identified as ~97% γ-valerolactone, with the minor products; levulinic acid, 3-methyl-2-cyclopentenone, and 2,3-dimethyl-2-cyclopentenone by using a combination of GC-MS and NMR spectroscopy
Robust gain-scheduling output feedback control of state-delayed lft systems using dynamic IQCS
No full textThis paper is concerned with the robust gain-scheduling output feedback control problem for a class of linear parametervarying systems with time-varying state delay. The controlled plant under consideration is described as a linear fractional transformation (LFT) model of scheduling parameters. Dynamic integral quadratics (IQCs) are employed to characterize the input-output behavior of the state-delay nonlinearity. The robust stability and the L2-gain performance are first analyzed using quadratic Lyapunov function. Then, the design of dynamic output-feedback controllers robust against the plant state-delay nonlinearity and gain-scheduled by parameters is examined. The synthesis conditions of such robust gain-scheduling controllers are formulated in terms of linear matrix inequalities (LMIs) plus a line search, which can be solved effectively using existing algorithms. A numerical example has been used to demonstrate the effectiveness and advantages of the proposed approach
The impact of frequency of behavior and type of contact on judgments involving a criminal stalking case
No full textWe investigated mock juror perceptions of the frequency of behavior and type of contact in an ex-intimate stalking case. We used a mock-juror methodology, in which 204 community members (129 women) read a stalking trial summary, rendered a verdict, and evaluated the intent of the defendant to cause the victim fear and distress, as well as the victims experience with these emotions. The trial varied as to whether there were 5 or 30 stalking incidents and whether the stalking involved personal contact or stalking via text message. Results showed that females were more likely to render a guilty verdict when the victim had been stalked 30 times rather than 5 times while males were equally likely to render a guilty verdict regardless of the frequency. Mock jurors were significantly more likely to render guilty verdicts in the personal contact condition than in the text message condition. Females perceptions of the victims fear and distress mediated the frequency of incidents x gender interaction. The victims fear and the defendants intentions mediated the main effect of type of contact on verdict. Cognitive network analyses showed that victim fear and the defendants intent to cause fear were central to participant verdict decision making. We discuss these results in terms of the implications, specifically that victim fear should be a primary focus in stalking legislation
Determination of withdrawal time for oxytetracycline in different types of goats for milk consumption
No full textAntibiotics are widely used in animal husbandry and the presence of antibiotics in milk is a health hazard. The objective of this study was to determine residual amounts of oxytetracycline in fresh, aged, and pasteurized milk of 3 breeds of goats using HPLC analysis. It was also essential to determine the safe withdrawal period of oxytetracycline in lactating goats. The quantitative results obtained using the HPLC system were compared with the tolerance limit of oxytetracycline in milk in the United States. Fifteen milking does, 5 Nubians, 5 Alpines, and 5 LaManchas were randomly selected from the milking herd at the International Goat Research Center at Prairie View A&M University. A simple sample preparation and isocratic HPLC method using ultraviolet detection was used for analysis of milk samples. The HPLC results indicated that the withdrawal period of oxytetracycline in treated Alpine does was 82. h (7 milking), whereas for Nubian does the period was 58. h (5 milking), and for LaManchas the period was 72. h (6 milking) after drug administration. The overall withdrawal period for all the treated goats of 3 breeds was 72. h. Although these results indicated that the depletion rate of this antibiotic was faster in goats than the reported data for cows, the 96-h withdrawal period that is currently used for lactating cows is still necessary for these 3 breeds of goats. Additionally, our results indicated that oxytetracycline is not stable in goat milk at refrigeration temperature or during pasteurization and will decrease significantly
Determination of withdrawal time for oxytetracycline in different types of goats for milk consumption
No full textAntibiotics are widely used in animal husbandry and the presence of antibiotics in milk is a health hazard. The objective of this study was to determine residual amounts of oxytetracycline in fresh, aged, and pasteurized milk of 3 breeds of goats using HPLC analysis. It was also essential to determine the safe withdrawal period of oxytetracycline in lactating goats. The quantitative results obtained using the HPLC system were compared with the tolerance limit of oxytetracycline in milk in the United States. Fifteen milking does, 5 Nubians, 5 Alpines, and 5 LaManchas were randomly selected from the milking herd at the International Goat Research Center at Prairie View A&M University. A simple sample preparation and isocratic HPLC method using ultraviolet detection was used for analysis of milk samples. The HPLC results indicated that the withdrawal period of oxytetracycline in treated Alpine does was 82. h (7 milking), whereas for Nubian does the period was 58. h (5 milking), and for LaManchas the period was 72. h (6 milking) after drug administration. The overall withdrawal period for all the treated goats of 3 breeds was 72. h. Although these results indicated that the depletion rate of this antibiotic was faster in goats than the reported data for cows, the 96-h withdrawal period that is currently used for lactating cows is still necessary for these 3 breeds of goats. Additionally, our results indicated that oxytetracycline is not stable in goat milk at refrigeration temperature or during pasteurization and will decrease significantly
Acidic ionic liquid catalyzed liquefaction of cellulose in ethylene glycol; Identification of a new cellulose derived cyclopentenone derivative
No full textCellulose can be liquefied in ethylene glycol at 180 °C, using 6.7 mol % 1-(1-alkylsulfonic)-3-methylimidazolium chloride ionic liquids as catalysts. The maximum liquefied product yields of 0.3436 and 0.3046 g/g of cellulose were achieved after 20 h at 180 °C using 1-(1-proylsulfonic)-3-methylimidazolium chloride and 1-(1-butylsulfonic)-3-methylimidazolium chloride as the catalysts. The liquefied oil produced from both ionic liquid catalysts had similar compositions. Unlike in previously reported mineral acid catalyzed cellulose liquefactions, the new catalysts give stable oils with well-defined compositions of only three compounds. The three compounds in the oil were identified as 2-hydroxyethyl levulinate, 2-hydroxyethyl levulinate ethylene ketal, and 2,3,6,7-tetrahydro-cyclopenta[1,4]dioxin-5-one using GC-MS, HRMS, and 1H, 13C, and 1H-1H COSY NMR spectroscopy. The third product 2,3,6,7-tetrahydro-cyclopenta[1,4]dioxin-5-one is a new C-6 carbohydrate derived cyclopentenone derivative, identified for the first time in a cellulose liquefaction process. The composition of the three components reaches a steady state after 20 h of reaction at 180 °C with a 2-hydroxyethyl levulinate:2-hydroxyethyl levulinate ethylene ketal:2,3,6,7-tetrahydro-cyclopenta[1,4]dioxin-5-one molar percentage ratio of approximately 47:22:31
Kink, singular soliton and periodic solutions to class of nonlinear equations
Get PDFIn this paper, we extend the ordinary differential Duffing equation into a partial differential equation. We study the traveling wave solutions to this model by using the G\u27/G expansion method. Then, based on the obtained results given for the Duffing equation, we generate kink, singular soliton and periodic solutions for a coupled integrable dispersionless nonlinear system. All the solutions given in this work are verified