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This paper is concerned with the relative controllability for a class of dynamical control systems described by semilinear fractional stochastic dierential equations with nonlocal conditions in Hilbert space. Sucient conditions for relative controllability results are obtained using Schaefer's xed point theorem. An example is provided to show the application of our result

The study of ill-posed abstract Volterra equations is a recent subject. In this paper, we investigate equations on the line, continue the research of (a, k)-regularized C-resolvent families, subordination principles, abstract semilinear Volterra integrodifferential equations, and provide several illustrative examples.

The Sylvester equation has numerous applications in control and system theory, power system, linear algebra, model reduction and signal processing. In the present paper, a global transpose-free quasi- minimal residual method for the Sylvester equations is proposed. The resulting method, with short- term recurrences, does not involve the multiplication with the transpose of the coefficient matrices, and often exhibits smoother convergence behavior than some other existing global methods. Finally, several numerical examples are reported by comparing the proposed method with some global methods.

In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a class of variational-hemivariational inequalities with perturbations in Banach spaces, which includes as a special case the class of mixed variational inequalities. Under very mild conditions, we establish some metric characterizations for the well-posed variational-hemivariational inequality, and show that the well-posedness by perturbations of a variational-hemivariational inequality is closely related to the well-posedness by perturbations of the corresponding inclusion problem. Furthermore, in the setting of finite-dimensional spaces we also derive some conditions under which the variational-hemivariational inequality is strongly generalized well-posed-like by perturbations.

In this paper, optimal control for stochastic singular integro-differential Takagi-Sugeno (T-S) fuzzy system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of MRDE is computed by solving differential algebraic equation (DAE) using a novel and nontraditional ACP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. An illustrative numerical example is presented for the proposed method.

In this paper we present some bounds of an approximate solution to variational and quasi-variational inequalities. The measures of errors can be used for construction of iterative and continuous procedures for solving variational (quasi-variational) inequalities and formulation of corresponding stopping rules. We will also present some methods based on linearization for solving quasi-variational inequalities.

In this paper we get estimation of the absolute condition number a Hilbert space operator, which is related with the outer generalized inverse of a given operator.

In this paper we study the Gilpin-Ayala competition system with random perturbation which is more general and more realistic than the classical Lotka-Volterra competition model. We verify that the positive solution of the system does not explode in a finite time. Furthermore, it is stochastically ultimately bounded and continuous a.s. We also obtain certain results about asymptotic behavior of the stochastic Gilpin-Ayala competition model. 2010 Mathematics Subject Classifications. 60H10, 34K50. .

Problems which relate to production, health and reproduction in herds of high yielding cows very often occur due to insufficient knowledge and monitoring of energy reserves in cow organisms. Many researches and practical experiences in this field indicate significant relation between body condition and achieved results in production. Body condition of heads of cattle in certain stages of production cycle is important parameter of applied nutrition, but also entire technological procedure. In countries with developed cattle production, evaluation of body condition has for several years been main component of production practice on farms. It is considered that condition is very reliable indicator of the nutrition status and energy balance in the organism. Body condition score is subjective and practical method which enables precise assessment of deposited fat in the cow organism by observing and touching previously determined body regions and fields. There is considerable variability of the condition of cows in different stages of production cycle. Body condition of high yielding cows often comes out of the frame of optimal values for certain stage of production cycle. Decrease of production, disorders in health condition and fertility of cows indicate the nature of relation between inadequate body condition and stated problems. Shape and strength of the relation between production results and body condition score confirms its reliability. This is all indication of the need for wider application of this evaluation system. Based on body condition score, beside other important factors in the production cycle, there is realistic possibility to achieve more efficient production of milk from the aspect of energy. Main purpose of this paper was to present how the application of methods for body condition score and its significance for production practice can be functional. Postojeći problemi u proizvodnji mleka, rezultatima reprodukcije i zdravstvenom stanju visokoproizvodnih krava mogu da se dovedu u vezu sa primenjenom tehnologijom ishrane. Važno pitanje u tehnologiji ishrane visokomlečnih krava predstavlja količina raspoložive energije (hrana, depoi masti, mišići) u ključnim fazama proizvodnog ciklusa (period zasušenja i rane laktacije). Deficit energije u kritičnim periodima proizvodnog procesa može da dovede do ozbiljnih poremećaja u proizvodnji, zdravlju i reprodukciji U početnoj fazi proizvodnje mleka najkritičniji je period maksimalne dnevne proizvodnje. Negativan bilans energije najizraženiji je u vrhu laktacije. Visok gubitak energije na račun telesnih rezervi predstavlja veliko opterećenje za metabolizam krava. Obezbeđenje adekvatne količine energije je složen uslov za svaku fazu proizvodnog ciklusa. OTK je subjektivan metod koji vizuelno i opipavanjem vrednuje količinu potkožne telesne masti. OTK je koristan alat za upravljanje mlečnim stadom. Idealna telesna kondicija je rang koji je u funkciji toka i faze laktacije. Procena rezervi energije u organizmu utvrđena preko OTK u osnovi predstavlja hranidbeni status grla vrednovan preko deponovanog masnog tkiva, pri čemu telesni okvir i masa grla imaju sekundaran značaj. Jedan od sistema za OTK krava koji je značajan za praksu je američki Virdžinija sistem modifikovan po Edmodsonu. Sistem za OTK kreiran je u obliku mape (karte) za ocenu visokomlečnih krava. Mapa je precizno pripremljena za svaki telesni region i polje koji se može smatrati važnim u dodeli ukupne OTK krave. Tri velika telesna regiona (slabine, karlica i koren repa) podeljena su osam polja na telu krave (slabine imaju četiri polja; karlica ima tri polja; koren repa ima jedno polje). Svako telesno polje se posebno ocenjuje i koristi kao pokazatelj telesne kondicije. Svako grlo ocenjeno je individualno za promene nivoa ocene duž skale od 1 do 5. Kontinuirano se koristi povećanje od 0,25 delova poena. Ceo sistem OTK funkcioniše sa 17 nivoa u okviru ukupne skale ocena posmatrane u intervalu od minimalne ocene u iznosu 1 i maksimalne u iznosu 5. Ocena 1 pokazuje mršavu kondiciju. Ocena 5 pokazuje izrazito tovnu kondiciju. Svaka faza proizvodnog ciklusa ima svoju optimalnu ocenu. Pod normalnim uslovima krave treba da gube telesnu kondiciju najviše od 4 do 6 nedelja. U skromnim vrednostima telesna kondicija postepeno se vraća u periodu od 7 do 12 nedelje. Krave u prvih od 100 do 120 dana laktacije treba da imaju ocenu između od 2,50 do 3,25. Ocena telesne kondicije od 200 dana laktacije do perioda zasušenja treba da je između 2,75 i 3,50. Ishrana u periodu zasušenja treba da osigura ocenu između 3,25 i 3,50. Mogućnost vrednovanja energetskog (hranidbenog) statusa i efikasnosti ishrane visokomlečnih krava pomoću OTK preporučuje ovaj sistem za praktičnu primenu u tehnološkim programima na govedarskim farmama.

Condition numbers play an important role in numerical analysis. Classical condition numbers are norm-wise: they measure both input perturbations and output errors with norms. To take into account the relative scaling of data components or a possible sparseness, component-wise condition numbers have been increasingly considered. In this paper, we give explicit expressions for the mixed and component-wise condition numbers for the weighted Moore-Penrose inverse of a matrix A, as well as for the solution and residue of a weighted linear least squares problem ||W 1 2 (Ax-b) ||2 = minv2Rn ||W 1 2 (Av-b) ||2, where the matrix A with full column rank. .

The aim of this paper is to study the existence and uniqueness of solutions for a general stochastic integrodifferential equation of the Ito type, by using the concept of non-linear bounded random integral contractors, which includes the Lipschitz condition as a special case. The method applied in this consideration follows partially the basic ideas of the contractor theory introduced earlier by Altman [1, 2] and Kuo [6]. It is also shown that the Lipschitz condition and the condition based on a bounded random integral contractor for the coefficients of the considered equation, in general, cannot be compared.

The comparison of differential operators is a problem that was formulated in sixties by Lars Hormander, it is a part of the theory of partial differential operators with constant coefficients, this problem up to now does not have a complete solution. The urgency of this problem is stipulated by the applications of the solvability theory of differential equations in special spaces of generalized functions. In this paper we prove some results in the manifold linearity of a polynomial, these results play an important role in the comparison of two linear partial differential operators problem.