Some geometrical methods, the so called Triangular Schemes and Principles, are introduced and investigated for weak congruences of algebras. They are analogues of the corresponding notions for congruences. Particular versions of Triangular Schemes are equivalent to weak congruence modularity and to weak congruence distributivity. For algebras in congruence permutable varieties, stronger properties—Triangular Principles—are equivalent to weak congruence modularity and distributivity.
It is proved in this paper that special generalized ultrametric and special $\mathcal U$ matrices are, in a sense, extremal matrices in the boundary of the set of generalized ultrametric and $ \mathcal U$ matrices, respectively. Moreover, we present a new class of inverse $M$-matrices which generalizes the class of $\mathcal U$ matrices.
We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner.
In this paper we introduce a new class of functions called weakly (µ, λ)-closed functions with the help of generalized topology which was introduced by Á. Császár. Several characterizations and some basic properties of such functions are obtained. The connections between these functions and some other similar types of functions are given. Finally some comparisons between different weakly closed functions are discussed. This weakly (µ, λ)- closed functions enable us to facilitate the formulation of certain unified theories for different weaker forms of closed functions.
We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given.
In this investigation, a new algorithm is developed for the updating of a neural network. It is concentrated in a fuzzy transition between the recursive least square and extended Kalman filter algorithms with the purpose to get a bounded gain such that a satisfactory modeling could be maintained. The advised algorithm has the advantage compared with the mentioned methods that it eludes the excessive increasing or decreasing of its gain. The gain of the recommended algorithm is uniformly stable and its convergence is found. The new algorithm is employed for the modeling of two synthetic examples.
There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via "standard approaches'' such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large-scale long-time hydrogeological calculations. In the article, a new approach to the modelling of groudwater flow in fractured porous medium, which combines the above-mentioned models, is described. This article presents the mathematical formulation and demonstration of numerical results obtained by this new approach. The approach considers three substantial types of objects within a structure of modelled massif important for the groudwater flow - small stochastic fractures, large deterministic fractures, and lines of intersection of the large fractures. The systems of stochastic fractures are represented by blocks of porous medium with suitably set hydraulic conductivity. The large fractures are represented as polygons placed in 3D space and their intersections are represented by lines. Thus flow in 3D porous medium, flow in 2D and 1D fracture systems, and communication among these three systems are modelled together.
Multimedia social networks (MSNs) provide great convenience to users, while privacy leaks issues are becoming prominent. The studies on relationship-based access control have been widely used in social networks. However, with the dynamic development of social networks and rapid growth of user information, the access control does not completely meet the current system's need. In this paper, an attribute-based access control model called ABAC{MSN is proposed for MSNs. This model comprehensively considers user attributes, environment attributes and resource attributes, not only including relationships among users. In this model, users can set multimedia usage control policies based on three categories of user-defined attributes. A formal theoretical model is established, which includes constraint rules, data ow rules, policy conflict resolution mechanism, and applied to CyVOD.net, a multimedia social-network-platform prototype systems. The deployment and application denote that this method effectively and exibly addresses use-case scenarios of multi-attribute-based media access control, and improves the access security of social media platforms and resources.