Among the programmes aimed at developing a standard model for properties and state of the Earth’s crystalline crust, those dealing with drilling the Kola (SG-3), Ural (SG-4) and German (KTB) superdeep boreholes yielded the most interesting results. No marked depth dependence of rock volume density and seismic wave velocities was observed in the sections of SG-3 and SG-4. A new result of the investigations is the discovery of strongly anisotropic rocks in the SG-3, SG-4 and KTB sections. In the massifs of the Kola and German superdeep boreholes such rocks constitute the majority of the drilled sections. The presence of the velocity anisotropy as well as the complex structure of the rocks composing crystalline metamorphosed sequences greatly hamper the interpretation of the results obtained from the seismic survey conducted at the surface., Felix F. Gobratsevich., and Obsahuje bibliografii
In this paper we derive new properties complementary to an $2n \times 2n$ Brualdi-Li tournament matrix $B_{2n}$. We show that $B_{2n}$ has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of $B_{2n}$ is also determined. Related results obtained in previous articles are proven to be corollaries.
In the paper the problem of mathematical properties of B-operations and weak WB-operations introduced by the author for interpretation of connectives "and'', "or'', and "also'' in fuzzy rules is considered. In previous author's papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system described by set of rules of the type if - then. Monotonicity condition, required for triangular norms, is replaced by condition of positivity (negativity), i. e. operations must be only positively (negatively) defined. Weak B-operations may not fulfill associativity condition.
By making use of the known concept of neighborhoods of analytic functions we prove several inclusions associated with the $(j,\delta )$-neighborhoods of various subclasses of starlike and convex functions of complex order $b$ which are defined by the generalized Ruscheweyh derivative operator. Further, partial sums and integral means inequalities for these function classes are studied. Relevant connections with some other recent investigations are also pointed out.
We study some properties of generalized reduced Verma modules over $\mathbb{Z}$-graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for $\mathbb{Z}$-graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules., Keli Zheng, Yongzheng Zhang., and Obsahuje bibliografické odkazy
Quaternion algebras ( −1,b ⁄ ℚ ) are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.
In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space $X$ and a subspace $Y$ satisfy that $Y\subset \overline {{\rm Int} Y}$ and $Y$ is strongly pseudocompact and metacompact in $X$, then $Y$ is compact in $X$. We also give an example to demonstrate that the condition $Y\subset \overline {{\rm Int} Y}$ can not be omitted.
We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.
Generalization phenornena which také plače in two different assembly neural networks are considered in the paper. Either of these two assembly networks is artificially partitioned into several subiietworks according to the number of classes that the network has to recognize. Hebb’s cissernblies are formed in the networks. One of the assembly networks is with binary connections, the other is with analog ones. Recognition abilities of the networks are compared on the task of handwritten character recognition. The third neural network of a perceptron type is considered in the paper for comparison with the previous ones. This latter network works according to the nearest-neighbor method. Computer simulation of all three neural networks was performed. Experirnents showed that the assembly network with binary connections has approximately the same recognition accuracy as the network realizing the nearest-neighbor technique.
The distance Laplacian of a connected graph $G$ is defined by $\mathcal {L} = {\rm Diag(Tr)}- \mathcal {D}$, where $\mathcal {D}$ is the distance matrix of $G$, and ${\rm Diag(Tr)}$ is the diagonal matrix whose main entries are the vertex transmissions in $G$. The spectrum of $\mathcal {L}$ is called the distance Laplacian spectrum of $G$. In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties of the distance Laplacian spectrum that enable us to derive the distance Laplacian characteristic polynomials for several classes of graphs.