Abstract: Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., RH = R = R−1 = ±Im and SH = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize AX−Z2+Y HA−WH2, and, given an arbitrary A˜ ∈ Cm×n, we find a unique matrix among the minimizers of AX − Z2 + Y HA − WH2 in ρ that minimizes A − A˜. We also obtain sufficient and necessary conditions for existence of A ∈ ρ such that AX = Z, Y HA = WH, and characterize the set of all such matrices A if the conditions are satisfied. These results are applied to solve a class of left and right inverse eigenproblems for generalized reflexive (anti-reflexive) matrices.
Abstract: In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.
Abstract: In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.
Abstract: Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.
Abstract: The presented paper copes with an experimental evaluation of a model based on modified Weibull size effect theory. Classical statistical Weibull theory was modified by introducing a new parameter (correlation length lp) representing the spatial autocorrelation of a random mechanical properties of material. This size effect modification was observed on two different materials used in civil engineering: unreinforced (plain) concrete and multi-filament yarns made of alkaliresistant (AR) glass which are used for textile-reinforced concrete. The behavior under flexural, resp. tensile loading was investigated by laboratory experiments. A high number of specimens of different sizes was tested to obtain statistically significant data which were subsequently corrected and statistically processed. Due to a distortion of the measured displacements caused by the unstiff experiment device, only the maximal load values were statistically evaluated. Results of the experiments showed a decreasing strength with an increasing sample length. Size effect curves were obtained and the correlation length was fitted according to measured data. Results did not exclude the existence of the proposed new parameter lp.
Abstract: As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change
signs in this paper, which are different from the corresponding ones of known literature.
Abstract: By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic
solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and effectiveness of the results.
Abstract: In this paper, the three species food chain model on time scales is established. The Monod–Haldane functional response and time delay are considered. With the help of coincidence degree theory, existence of periodic solutions is investigated, which unifies the continuous and discrete analogies.
Abstract: In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.
Abstract: In this letter, we considers a delayed predatory-prey system with Holling type II functional response. Under some sufficient conditions, the existence of multiple positive periodic solutions is obtained by using Mawhin’s continuation theorem of coincidence degree theory. An example is given to illustrate the effectiveness of our results.
Abstract: In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given.
Abstract: This paper is concerning the application of a deterministic decisional pattern to a multi-agent system which would provide intelligence to a distributed energy smart grid at local consumer level. Development of multi-agent application involves agent specifications, analysis, design and realization. It can be implemented by following several decisional patterns. The purpose of present article is to suggest a new approach to control the smart grid system in a decentralized competitive approach. The proposed algorithmic solution results from a deterministic dichotomous approach based on environment observation. It uses an iterative process to solve automatic learning problems. Through memory of collected past tries, the algorithm monotonically converges to very steep system operation point in attraction basin resulting from weak system nonlinearity. In this sense, system is given by (local) constitutive elementary rules the intelligence of its global existence so that it can self-organize toward optimal operating sequence.
Abstract: In this paper, by constructing a special cone and using
fixed point theorem and fixed point index theorem of cone, we get the
existence of positive solution for a class of singular eigenvalue value
problems with p-Laplace operator, which improved and generalized
the result of related paper.
Abstract: The degrading effect due to bacterial growth on the structural integrity of concrete floor surfaces is predictable; this consequently cause development of surface micro cracks in which organisms penetrate through resulting in surface spalling. Hence, the need to develop mix design meeting the requirement of floor surfaces exposed to aggressive agent to improve certain material properties with good workability, extended lifespan and low cost is essential. In this work, tests were performed to examine the microbial activity on kitchen floor surfaces and the effect of adding admixtures. The biochemical test shows the existence of microorganisms (E.coli, Streptococcus) on newly casted structure. Of up to 6% porosity was reduced and improvement on structural integrity was observed upon adding mineral admixtures from the concrete mortar. The SEM result after 84 days of curing specimens, shows that chemical admixtures have significant role to enable retard bacterial penetration and good quality structure is achieved.
Abstract: In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.
Abstract: We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.
Abstract: In this paper, the existence, multiplicity and
noexistence of positive solutions for a class of semipositone
discrete boundary value problems with two parameters is
studied by applying nonsmooth critical point theory and
sub-super solutions method.
Abstract: Steganography is the process of hiding one file inside another such that others can neither identify the meaning of the embedded object, nor even recognize its existence. Current trends favor using digital image files as the cover file to hide another digital file that contains the secret message or information. One of the most common methods of implementation is Least Significant Bit Insertion, in which the least significant bit of every byte is altered to form the bit-string representing the embedded file. Altering the LSB will only cause minor changes in color, and thus is usually not noticeable to the human eye. While this technique works well for 24-bit color image files, steganography has not been as successful when using an 8-bit color image file, due to limitations in color variations and the use of a colormap. This paper presents the results of research investigating the combination of image compression and steganography. The technique developed starts with a 24-bit color bitmap file, then compresses the file by organizing and optimizing an 8-bit colormap. After the process of compression, a text message is hidden in the final, compressed image. Results indicate that the final technique has potential of being useful in the steganographic world.
Abstract: Research on the boron (B) toxicity problems had recently considerable relation, especially in the dry regions of the world. Development of resistant varieties to B toxicity is a high priority on these regions, where the soils have high levels of B. Thus, this study aimed to assessment the resistance of wheat genotypes to B toxicity using the agronomic and physiologic parameters. For this aim, a pot experiment, based on a completely randomized design with three replications, was conducted using the soil of calcareous usthochrepts. In the study, twenty different wheat genotypes of T. aestivum and T. Durum were used. Boron fertilizer at the levels of 0 (-B), 30 mg B kg-1 (+B) as H3BO3 was applied to the pots. After harvest, plant dry matter yield was recorded, and total B concentrations in tops of wheat plants were determined. The results have revealed the existence of a large genotypic variation among wheat genotypes to their physiologic and agronomic susceptibility to B toxicity.
Abstract: Petroglyphs, stone sculptures, burial mounds, and
other memorial religious structures are ancient artifacts which find
reflection in contemporary world culture, including the culture of
Kazakhstan. In this article, the problem of the influence of ancient
artifacts on contemporary culture is researched, using as an example
Kazakhstan-s sculpture and painting. The practice of creating
petroglyphs, stone sculptures, and memorial religious structures was
closely connected to all fields of human existence, which fostered the
formation of and became an inseparable part of a traditional
worldview. The ancient roots of Saka-Sythian and Turkic nomadic
culture have been studied, and integrated into the foundations of the
contemporary art of Kazakhstan. The study of the ancient cultural
heritage of Kazakhstan by contemporary artists, sculptors and
architects, as well as the influence of European art and cultures on the
art of Kazakhstan are furthering the development of a new national
art.