The failure of available physical sensors for the online measurement of protein concentration in cells is a key problem to understanding the transition in bio-systems. In this paper, a new state observer has been designed to estimate three protein concentrations by using a gene-expression mathematical model. Interestingly, its only input is the concentration of one messenger RNA (mRNA). Similarly by differential-algebraic observability analysis is showed that the gene-expression model is indeed observable. The observer convergence was demonstrated by analysing the estimation error dynamics. In silico experiments confirm the satisfactory performance of this new observer.

}, keywords = {34A34, 92B05, 93B07, 93E10}, issn = {1056-2176}, doi = {10.12732/dsa.v27i3.5}, url = {https://acadsol.eu/dsa/articles/27/3/5.pdf}, author = {RICARDO AGUILAR-LOPEZ and JUAN MATA-MACHUCA} } @article {403, title = {ON THE OSCILLATION OF THREE DIMENSIONAL alpha-FRACTIONAL DIFFERENTIAL SYSTEMS}, journal = {Dynamic Systems and Applications}, volume = {27}, year = {2018}, month = {11/2018}, pages = {22}, chapter = {873}, abstract = {In this article, we consider the three dimensional $\alpha$-fractional nonlinear differential system of the form $$ D^{\alpha}\left(x(t)\right)=a(t)f\left(y(t)\right), $$ $$ D^{\alpha}\left(y(t)\right)=-b(t)g\left(z(t)\right), $$ $$ D^{\alpha}\left(z(t)\right)=c(t)h\left(x(t)\right),\quad t \geq t_0, $$ where $0 \< \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We establish some new sufficient conditions for the oscillation of the solutions of the differential system, using the generalized Riccati transformation and inequality technique. Examples illustrating the results are also given.

}, keywords = {34A08, 34A34, 34K11}, issn = {1056-2176}, doi = {10.12732/dsa.v27i4.12}, url = {https://acadsol.eu/dsa/articles/27/4/12.pdf}, author = {G.E. CHATZARAKIS and M. DEEPA and N. NAGAJOTHI and V. SADHASIVAM} } @article {272, title = {OSCILLATORY BEHAVIOR OF ODD-ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH A NONPOSITIVE NEUTRAL TERM}, journal = {Dynamic Systems and Applications}, volume = {27}, year = {2018}, month = {01/2018}, pages = {12}, chapter = {125}, abstract = {In this paper, sufficient conditions are established for oscillation of all\ solutions of the odd-order nonlinear differential equations with a nonpositive neutral\ term. When the neutral term is present, all the results are new even for $n = 3$. An\ example is given to illustrate the main results.

}, keywords = {34C10, 34K11}, isbn = {1056-2176}, doi = {10.12732/dsa.v27i1.6}, url = {https://acadsol.eu/dsa/articles/27/1/6.pdf}, author = {GRACE, SAID R and JADLOVSKA, IRENA} } @article {78, title = {ON OCCURRENCE OF COMPLETE BLOW-UP OF THE SOLUTION FOR A DEGENERATE SEMILINEAR PARABOLIC PROBLEM WITH INSULATED BOUNDARY CONDITIONS}, journal = {Dynamic Systems and Applications}, volume = {24}, year = {2015}, month = {2015}, pages = {14}, chapter = {83}, abstract = {Let a, σ, p, q, r, and m be constants with a \> 0, σ \> 0, p >= 0, q >= 0, r \> 1, and m \> 0. This article studies the following degenerate semilinear parabolic initial-boundary value problem, ξ quτ - uξξ = ξ pu r for 0 \< ξ \< a, 0 \< τ \< σ, u(ξ, 0) = u0 (ξ) = m for 0 <= ξ <= a, uξ(0, τ) = 0 = uξ(a, τ) for τ \> 0. We derive criteria for u to blow up in finite time, and estimate the blow-up rate. We show that the blow-up is regional if q \> p; the blow-up is complete if q = p; and the blow-up cannot be complete if p \> q.

}, keywords = {35K57, 35K60, 35K65}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/24/06-dsa-83-96.pdf}, author = {NADEJDA E. DYAKEVICH} } @article {85, title = {OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT IN JUMP DIFFUSION MARKETS WITH NO SHORT-SELLING AND NO BORROWING}, journal = {Dynamic Systems and Applications}, volume = {24}, year = {2015}, month = {2015}, pages = {17}, chapter = {169}, abstract = {The optimal reinsurance and investment problem for insurance has attracted a lot of attention of researchers in the field of stochastic control for a long time. Along this line we discuss this problem in the case of jump diffusion markets when neither short-selling nor borrowing is allowed. Here, we specifically assume that the risk process of the insurance company is a diffusion process. The insurance company can transfer its risk by reinsurance and also invest its surplus in the financial market, where we model the price of the risky asset by a geometric L{\textasciiacute}evy process. To maximize the CARA (Constant Absolute Risk Aversion) utility of terminal wealth, the HJB equation with no short-selling constraint has been considered, and we obtain the closed form of the value function by a standard method. However, only a handful of people have discussed this problem under both constraints, (i.e. no short-selling and no borrowing). This is because the problem is much more general in this context, and becomes so complex that analytical solution could hardly be obtained. Therefore, we provide, under the no short-selling and no borrowing constraints, a numerical solution via Markov chain approximation, which proves to be effective and amenable.

}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/24/13-dsa-169-186.pdf}, author = {ZHANG JINGXIAO and CAO KAI and D. KANNAN} } @article {41, title = {OPTIMAL DIVIDEND AND REINSURANCE UNDER THRESHOLD STRATEGY}, journal = {Dynamic Systems and Applications}, volume = {20}, year = {2011}, month = {2011}, pages = {12}, chapter = {193}, abstract = {We consider the optimal dividend and reinsurance problems in this article, where the dividend strategy is the threshold strategy and the reinsurance is the proportional reinsurance. Despite the fact that the barrier strategy has its popularity in theoretical research, such a strategy has little practical acceptance as it will lead to the certainty of ultimate ruin. A modified version of the barrier strategy is the threshold strategy which assumes that dividends are paid at a rate smaller than the rate of premium income whenever the surplus is above some threshold level, and that no dividends are paid out whenever the surplus is below the threshold level. In this article, we consider two cases of the threshold strategy. One is the threshold strategy without barrier, and the other is the threshold strategy with barrier. The first case generalizes and corrects part of results in [16]. In the second case, we use the stochastic control theoretic techniques, to find the value function as well as the optimal investment-reinsurance policy in closed form.

}, keywords = {60H10, 60H30, 93E20}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/20/14-DSA-31-07.pdf}, author = {JINGXIAO ZHANG and SHENG LIU and D. KANNAN} } @article {67, title = {OPTIMAL DIVIDEND PROBLEM WITH THE INFLUENCE OF DIVIDEND PAYOUTS ON INSURANCE BUSINESS}, journal = {Dynamic Systems and Applications}, volume = {20}, year = {2011}, month = {2011}, pages = {12}, chapter = {519}, abstract = {This article initiates the optimal dividend problem, from the view point of the managers of the insurance companies. where we incorporate the influence of dividend payouts on the insurance business. We begin with a mathematical characterization of the influence of dividend payouts, and then continue to find the optimal dividend policy that maximizes the expected utility of terminal wealth and minimizes the ruin probability. We study the problem in terms of the Levy process and derive the diffusion process case as a particular one.

}, keywords = {60H10, 60H30, 93E20}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/20/34-DSA-31-21.pdf}, author = {JINGXIAO ZHANG and SHENG LIU and D. KANNAN} } @article {38, title = {OPTIMAL FEEDBACK CONTROL LAW FOR A CLASS OF PARTIALLY OBSERVED UNCERTAIN DYNAMIC SYSTEMS: A MIN-MAX PROBLEM}, journal = {Dynamic Systems and Applications}, volume = {20}, year = {2011}, month = {2011}, pages = {19}, chapter = {149}, abstract = {In this paper we consider a class of partially observed dynamic systems with measurement uncertainty and present a technique for design of optimal linear output feedback controls to minimize the maximum risk. This is then extended to cover systems with uncertainty in the measurement as well as in the dynamics. These results are presented in the form of necessary conditions of optimality. Theoretical results are illustrated by numerical examples.

}, keywords = {Differential Inclusion, Necessary Conditions of Optimality, Optimal Feedback Control Law, Uncertain Nonlinear Dynamic systems}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/20/11-DSA-31-01.pdf}, author = {N. U. AHMED and M. SURUZ MIAH} } @article {42, title = {OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE UNDER NO SHORT-SELLING AND NO BORROWING}, journal = {Dynamic Systems and Applications}, volume = {20}, year = {2011}, month = {2011}, pages = {18}, chapter = {205}, abstract = {Insurance companies resort to investment and reinsurance, among other options, to manage their reseerves. This article addresses the problem of optimal investment and reinsurance when no short-selling and no borrowing allowed. More specifically, we assume that the risk process of the insurance company is a compound Poisson process perturbed by a standard Brownian motion and that the risk can be reduced through a proportional reinsurance. In addition, the surplus can be invested in the financial market such that the portfolio will consist, for simplicity, of one risky asset and one risk-free asset. Our goal is to find the optimal investment and reinsurance policy which can maximize the expected exponential utility of the terminal wealth. In the case of no short-selling, we find the closed form of value function as well as the optimal investment-reinsurance policy. In the case when neither short-selling nor borrowing allowed, the resulting HJB equation is difficult to solve analytically, and hence we provide a numerical solution through Markov chain approximation techniques

}, keywords = {60H10, 60H30, 93E20}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/20/15-DSA-31-10.pdf}, author = {JINGXIAO ZHANG and SHENG LIU and D. KANNAN} } @article {32, title = {ON THE OSCILLATION OF FOURTH ORDER SUPERLINEAR DYNAMIC EQUATIONS ON TIME SCALES}, journal = {Dynamic Systems and Applications}, volume = {20}, year = {2011}, month = {2011}, pages = {10}, chapter = {45}, abstract = {Some oscillation criteria for the oscillatory behavior of fourth order superlinear dynamic equations on time scales are established. Criteria are proved that ensure that all solutions of superlinear and linear equations are oscillatory. Many of our results are new for corresponding fourth order superlinear differential equations and fourth order superlinear difference equations.

}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/20/04-DSA-30-12.pdf}, author = {SAID R. GRACE and RAVI P. AGARWAL and SANDRA PINELAS} } @article {151, title = {OPTIMAL CONTROL FOR PREDATOR-PREY SYSTEM WITH PREY-DEPENDENT FUNCTIONAL RESPONSE}, journal = {Dynamic Systems and Applications}, volume = {19}, year = {2010}, month = {2010}, pages = {8}, chapter = {537}, abstract = {An optimal control problem is studied for a predator-prey system with logistic growth rate of the prey and a prey-dependent functional response of the predator. The control function has two components and signifies the rate of mixture between the individuals of the species. The form of the optimal control is determined according to Pontryagin{\textquoteright}s maximum principle. It is bang-bang and the number of switchings points depends on the choice of some specific parameters.

}, keywords = {34H05, 49K15, 92D25, 93C10, 93C15}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/19/37-DSA-249.pdf}, author = {N. C. APREUTESEI} } @article {148, title = {OPTIMAL FILTERING OF LINEAR SYSTEM DRIVEN BY FRACTIONAL BROWNIAN MOTION}, journal = {Dynamic Systems and Applications}, volume = {19}, year = {2010}, month = {2010}, pages = {19}, chapter = {495}, abstract = {In this paper, we consider a continuous time filtering of a multi-dimensional Langevin stochastic differential system driven by a fractional Brownian motion process. It is shown that this filtering problem is equivalent to an optimal control problem involving convolutional integrals in its dynamical system. Then, a novel approximation scheme is developed and applied to this optimal control problem. It yields a sequence of standard optimal control problems. The convergence of the approximate standard optimal control problem to the optimal control problem involving convolutional integrals in its system dynamics is established. Two numerical examples are solved by using the method proposed. The results obtained clearly demonstrate its efficiency and effectiveness.

}, keywords = {41A50}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/19/34-DSA-30-09.pdf}, author = {MASNITA MISIRAN and CHANGZI WU and ZUDI LU and K. L. TEO} } @article {132, title = {OSCILLATION CRITERIA FOR SECOND ORDER NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS}, journal = {Dynamic Systems and Applications}, volume = {19}, year = {2010}, month = {2010}, pages = {13}, chapter = {235}, abstract = {. Some new oscillation criteria are established for second order neutral partial functional differential equation of the form ∂ ∂t " r(t) ∂ ∂t u(x, t) +X l i=1 λi(t)u(x, t - τi) !$\#$= a(t)△u(x, t) +Xs k=1 ak(t)△u(x, t - ρk(t)) - q(x, t)u(x, t) - Xm j=1 qj (x, t)fj (u(x, t - σj )), (x, t) ∈ {\textohm} {\texttimes} [0, $\infty$) = G under the conditions R$\infty$ t0 r -1 (s)ds = $\infty$ and R$\infty$ t0 r -1 (s)ds \< $\infty$, respectively. where {\textohm} is a bounded domain in RN with a piecewise smooth boundary ∂{\textohm} and △ is the laplacian in the Euclidean N-space RN .

}, keywords = {34C10}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/19/18-DSA-248.pdf}, author = {RUN XU and FANWEI MENG} } @article {129, title = {OSCILLATION OF NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATION WITH SEVERAL COEFFICIENTS}, journal = {Dynamic Systems and Applications}, volume = {19}, year = {2010}, month = {2010}, pages = {11}, chapter = {199}, abstract = {In this article, we show that the oscillation of all solutions to the neutral equation [x (t) - R (t) N (x (t - κ))]' + Xn i=1 Pi (t) Fi (x (t - τi)) - Xm j=1 Qj (t) Gj (x (t - σj )) = 0 is implied by the oscillation of all solutions to the linear equation [x (t) - rx (t - κ)]' + Xn i=1 pix (t - τi) - Xm j=1 qjx (t - σj ) = 0. In these equations, R,Pi , Qj are positive and continuous functions, and κ, τi , σj are positive constants that represent delays

}, keywords = {34C10, 34K40, 34K99}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/19/15-DSA-239.pdf}, author = {MUSTAFA KEMAL YILDIZ} } @article {118, title = {OSCILLATIONS OF SCALAR NEUTRAL IMPULSIVE DIFFERENTIAL EQUATIONS OF THE FIRST ORDER WITH VARIABLE COEFFICIENTS}, journal = {Dynamic Systems and Applications}, volume = {19}, year = {2010}, month = {2010}, pages = {18}, chapter = {45}, abstract = {The theory of oscillations of neutral impulsive differential equations is gradually occupying a central place among the theories of oscillations of impulsive differential equations. This could be due to the fact that neutral impulsive differential equations play fundamental roles in the present drive to further develop information technology. Indeed, neutral differential equations appear in networks containing lossless transmission lines (as in high-speed computers where the lossless transmission lines are used to interconnect switching circuits). In this paper, we generalize and prove the results of oscillations of neutral delay differential equations with constant coefficients obtained by Gyori and Ladas for impulsive differential equations.

}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/19/04-DSA-04.pdf}, author = {I. O. ISAAC and Z. LIPSCEY} } @article {186, title = {OSCILLATION AND NONOSCILLATION OF FIRST-ORDER DYNAMIC EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS}, journal = {Dynamic Systems and Applications}, volume = {18}, year = {2009}, month = {2009}, pages = {12}, chapter = {363}, abstract = {In this article, we investigate oscillatory nature of all solutions of a class of delay dynamic equations including positive and negative coefficients. Also we give a nonoscillation criterion for this class of delay dynamic equations. While our results reduce to the well-known oscillation criteria for the particular cases of the time scale, they improve recent results on arbitrary time scales. Further, we give some illustrating examples as applications of our results

}, keywords = {34C10, 39A10}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/18/26-DSA-154.pdf}, author = {BASAK KARPUZ and {\"O}ZKAN {\"O}CALAN} } @article {187, title = {OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DAMPED DIFFERENTIAL EQUATIONS}, journal = {Dynamic Systems and Applications}, volume = {18}, year = {2009}, month = {2009}, pages = {17}, chapter = {375}, abstract = {By employing a class of kernel functions Φ (t, s, l) and a generalized Riccati technique, some new oscillation criteria are established for second-order nonlinear damped differential equations, which extend, improve and unify some related results known in the literature.

}, keywords = {34C10}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/18/27-DSA-156.pdf}, author = {YIN-LIAN FU and QI-RU WANG} } @article {191, title = {OSCILLATION OF SECOND ORDER NEUTRAL EMDEN-FOWLER DELAY DYNAMIC EQUATIONS OF MIXED TYPE}, journal = {Dynamic Systems and Applications}, volume = {18}, year = {2009}, month = {2009}, pages = {15}, chapter = {441}, abstract = {By means of generalized Riccati transformation and averaging technique, we establish some oscillation criteria for the second-order neutral Emden-Fowler delay dynamic equation of mixed type

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ( r(t)x^{∆}(t) )^{∆ }+ q_{1}(t) |y( δ(t) )|^{α-1} y( δ(t) ) + q_{2}(t) |y( δ(t) )|^{β-1} y( δ(t) ) = 0,

on a time scale T. Our results as a special case when T = R improve some well known oscillation criteria for second order neutral Emden-Fowler delay differential equation of mixed type, and when T = N, T = hN, and T = q^{No} , i.e., for neutral delay difference equations, neutral delay difference equations with constant step size, and q-neutral difference equations with variable step size. The results obtained here are essentially new and can be applied to different types of time scales. Some applications and examples are considered to illustrate the main results.

For linear Hamiltonian systems, even for self-adjoint second order differential systems, we obtain new oscillation results without the assumptions which have been required for related results given before. The main tool used is a generalized Riccati transformation and the standard integral averaging technique.

}, keywords = {34C10, 35A15}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/18/48-DSA-228.pdf}, author = {LIANZHONG LI and FANWEI MENG and ZHAOWEN ZHENG} } @article {251, title = {OPTIMAL CHOICE OF NONLINEAR OUTPUT FEEDBACK CONTROL LAW FOR A CLASS OF UNCERTAIN PARABOLIC SYSTEMS}, journal = {Dynamic Systems and Applications}, volume = {17}, year = {2008}, month = {2008}, pages = {12}, chapter = {571}, abstract = {In this paper we consider optimal output feedback boundary control problems for a class of semilinear uncertain parabolic systems. The uncertain initial boundary value problem is converted into an equivalent Cauchy problem described by a differential inclusion in appropriate Banach spaces. We follow game-theoretic formalism and prove existence of saddle points giving optimal strategies. This is an extension of a recent result of the author from linear to a class of nonlinear feedback operators. The paper is concluded with a brief description of open problems and future directions.

}, keywords = {47A62, 49J20, 49J24, 49N35, 65N21, 93B52, 93C20, 93C25}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/17/DSA-2007-571-582.pdf}, author = {N. U. AHMED} } @article {236, title = {OPTIMAL SENSOR SCHEDULING IN CONTINUOUS TIME}, journal = {Dynamic Systems and Applications}, volume = {17}, year = {2008}, month = {2008}, pages = {20}, chapter = {331}, abstract = {In this paper, we consider an optimal sensor scheduling problem in continuous time. This problem aims to find an optimal sensor schedule such that the corresponding estimation error is minimized. It is formulated as a deterministic optimal control problem involving both discrete and continuous valued controls. A computational method is developed for solving this deterministic optimal control problem based on a branch and bound method in conjunction with a gradient-based method. The branch and bound method is used to determine the optimal switching sequence of sensors, where a sequence of lower bound dynamic systems is introduced so as to provide effective lower bounds for the construction of the branching rules. For a given switching sequence, determining the respective optimal switching time is a continuous-valued optimal control problem and can be solved by gradient-based method with appropriate gradient formulae. This computational method is very efficient, as demonstrated by the numerical examples.

}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/17/DSA-2007-331-350.pdf}, author = {Z. G. FENG and K. L. TEO and V. REHBOCK} } @article {237, title = {OPTIMAL SENSOR SCHEDULING IN CONTINUOUS TIME}, journal = {Dynamic Systems and Applications}, volume = {17}, year = {2008}, month = {2008}, pages = {20}, chapter = {331}, abstract = {In this paper, we consider an optimal sensor scheduling problem in continuous time. This problem aims to find an optimal sensor schedule such that the corresponding estimation error is minimized. It is formulated as a deterministic optimal control problem involving both discrete and continuous valued controls. A computational method is developed for solving this deterministic optimal control problem based on a branch and bound method in conjunction with a gradient-based method. The branch and bound method is used to determine the optimal switching sequence of sensors, where a sequence of lower bound dynamic systems is introduced so as to provide effective lower bounds for the construction of the branching rules. For a given switching sequence, determining the respective optimal switching time is a continuous-valued optimal control problem and can be solved by gradient-based method with appropriate gradient formulae. This computational method is very efficient, as demonstrated by the numerical examples.

}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/17/DSA-2007-331-350.pdf}, author = {Z.G. FENG and K.L. TEO and V. REHBOCK} } @article {222, title = {OSCILLATION FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DAMPING}, journal = {Dynamic Systems and Applications}, volume = {17}, year = {2008}, month = {2008}, pages = {9}, chapter = {139}, abstract = {Some new oscillation criteria are given for second order nonlinear differential equations with damping of the form

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ( r(t) x{\textquoteright} ){\textquoteright}+ p(t) x{\textquoteright}+ q (t) f(x) = 0.\

Our results are to develop oscillation criteria without any restriction on the signs of p (t) and q (t). These results generalize and extend some earlier results of Abdullah [1] and Zheng and Liu [12].

}, keywords = {34C10, 34C15}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/17/DSA-2007-139-148.pdf}, author = {DEVRIM {\c C}AKMAK} } @article {259, title = {ON THE OSCILLATION OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION WITH POSITIVE AND NEGATIVE COEFFICIENTS}, journal = {Dynamic Systems and Applications}, volume = {17}, year = {2008}, month = {2008}, pages = {9}, chapter = {667}, abstract = {This paper is focused on the following nonlinear neutral differential equation with positive and negative coefficients

\ \ \ \ \ \ \ \ \ \ \ \ \ \ [ x(t) - R(t) f( x(t - r)) ]' + P(t) g(x(t - τ)) - Q(t )g( x(t - σ)) = 0,

where R(t), P(t), Q(t) ∈ C ([t_{0}, $\infty$), R^{+}),\ r \> 0,\ τ >= 0,\ σ >= 0. For this equation, oscillation criteria are established.

By using the functions of the form H(t, s) and a generalized Riccati technique, we establish new Kamenev-type and interval oscillation criteria for second-order nonlinear dynamic equations on time scales of the form

\ \ \ \ \ \ \ \ \ \ \ \ \ ( p(t)x^{∆}(t) )^{∆} + f( t, x(σ(t)) ) = 0.

The obtained interval oscillation criteria can be applied to equations with forcing term. Two examples are included to show the significance of the results.

}, keywords = {34C10, 39A10}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/17/DSA-2007-551-570.pdf}, author = {HAO HUANG and QI-RU WANG} } @article {289, title = {OPTIMAL FUSION OF SENSOR DATA FOR DISCRETE KALMAN FILTERING}, journal = {Dynamic Systems and Applications}, volume = {16}, year = {2007}, month = {2007}, pages = {14}, chapter = {393}, abstract = {In this paper we consider the question of optimal fusion of sensor data in discrete time. The basic problem is to design a linear filter whose output provides an unbiased minimum variance estimate of a signal process whose noisy measurements from multiple sensors are available for input to the filter. The problem is to assign weights to each of the sources (sensor data) dynamically so as to minimize estimation errors. We formulate the problem as an optimal control problem where the weight given to each of the sensor data is considered as one of the control variables satisfying certain constraints. There are as many controls as there are sensors. We develop an efficient method for determining the optimal fusion strategy and gives a numerical result for illustration.

}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/16/393-406-DSA-25-53-58\%20NU\%20Ahmed.pdf}, author = {Z.G. FENG and K.L. TEO and N.U. AHMED and Y. ZHAO and W.Y. YAN} } @article {266, title = {OPTIMIZATION OF THE MOTION OF A VISCO-ELASTIC FLUID VIA MULTIVALUED TOPOLOGICAL DEGREE METHOD}, journal = {Dynamic Systems and Applications}, volume = {16}, year = {2007}, month = {2007}, pages = {16}, chapter = {89}, abstract = {We consider the application of the topological degree theory for noncompact multivalued vector fields to the problem of existence of an optimal feedback control in the presence of delay for the model of the motion of a visco-elastic fluid satisfying the Voight rheological relation. The notion of a weak solution to the problem is introduced and the operator treatment of the problem allows to reduce it to the existence of a fixed point for a certain condensing multivalued map. We give an a priori estimate for solutions of the problem and the use of the degree method allows to prove the non-voidness and compactness of the solution set. As the result we obtain the existence of a solution minimizing the given quality functional.

}, keywords = {47H04, 47H09, 47H11, 76A05, 76A10, 76D55, 93B52, 93C20}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/16/089-104-Gori.pdf}, author = {C. GORI and V. OBUKHOVSKI and P. RUBBIONI and V. ZVYAGIN} } @article {292, title = {OSCILLATION OF LINEAR SECOND ORDER MATRIX DIFFERENTIAL SYSTEMS WITH DAMPING}, journal = {Dynamic Systems and Applications}, volume = {16}, year = {2007}, month = {2007}, pages = {17}, chapter = {433}, abstract = {In this paper, sufficient conditions have been obtained for the oscillation of a class of linear second order matrix differential systems with damping.

}, keywords = {34C10, 34K15}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/16/433-450-Meng.pdf}, author = {FANWEI MENG and CUIQIN MA} } @article {286, title = {OSCILLATION OF SECOND-ORDER DELAY AND NEUTRAL DELAY DYNAMIC EQUATIONS ON TIME SCALES}, journal = {Dynamic Systems and Applications}, volume = {16}, year = {2007}, month = {2007}, pages = {15}, chapter = {345}, abstract = {In this paper, we consider the second-order linear delay dynamic equation x ∆∆(t) + q(t)x(τ (t)) = 0, on a time scale T. We will study the properties of the solutions and establish some sufficient conditions for oscillations. In the special case when T = R and τ (t) = t, our results include some well-known results in the literature for differential equations. When, T = Z, T = hZ, for h \> 0 and T = Tn = {tn : n ∈ N0} where tn} is the set of the harmonic numbers defined by t0 = 0, tn = Pn k=1 1 k for n ∈ N0 our results are essentially new. The results will be applied on second-order neutral delay dynamic equations in time scales to obtain some sufficient conditions for oscillations. An example is considered to illustrate the main results.

}, keywords = {34A99, 34C10, 34K11, 39A10, 39A11, 39A99}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/16/345-360-DSA-26-18-Saker.pdf}, author = {S.H. SAKER} }