No 3-1 (2011)
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7-13 182
Abstract
We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We also present some authors results, which provide a solution for Seidel's problem on the volume of non-Euclidean tetrahedron.
13-18 187
Abstract
In the present paper geometric properties are investigated for a hyperbolic octahedron having rororo-symmetry.Trigonometrical identities connecting lengths ofedges and dihedral angles ofthe polyhedron under consideration are obtained (the sine-tangent theorem). It gives the key to express lengths through dihedral angles. Further, we find the volume of the octahedron in very important geometrical cases by making use the Schlafli formula.
19-34 163
Abstract
In this paper we formulate basic notions of homotopy topology, tell on hypothesis of Poincare and formulate D(2)-hypothesis. After that we remind some facts from combinatorial group theory, formulate the problem of gap relation and the problem of minimal normal generation. We mention connection between problems of this theory and problems of homotopy topology. In particular, it will be given a reformulation of Poincare's hypothesis in group terms and mention a connection between the problem of gap relation and the D'(2) -hypothesis. Then we offer the method that allows to show for some finite representations of groups that the number ofrelationship can't be reduced (the approach to a problem ofthe minimum normal generation).
34-38 234
Abstract
It's proposed the method for constructing minimal surfaces in Heisenberg group, endowed with Thurston's metric. The construction is based on Weierstrass type representation, and generating spinors of surface are expressed in terms of Baker-Akhiezer functions.
38-49 154
Abstract
We discuss some invariants of spatial graphs. We construct an invariant which has a structure of a Coxeter group. We give examples to show that this invariant distinguishes some spatial graphs.
50-57 177
Abstract
The notion of the Picard group of graph (also known as Jacobian group, sandpile group, critical group) was independently given by many authors. This is a very important algebraic invariant of a finite graph. In particular, the order ofthe Picard group coincides with the number ofspanning trees for a graph. The latter number is known for the simplest families of graphs such as Wheel, Fan, Prism, Ladder and Moebius ladder graphs. At the same time the structure of the Picard group is known only in several cases. The aim of this paper is to determine the structure of the Picard group of the Moebius ladder and Prism graphs.
58-63 198
Abstract
In this paper we study a class of closed orientable three-dimensional manifolds Mn(p, q) (n ^ 1, p ^ 3, 0 < q < p and (p, q) - 1) defined via pairwise identifications of the faces of fundamental polyhedra and having a cyclic symmetry. Using Heegaard diagram of Mn(p, 1), we obtain upper bounds for their Matveev complexity.
63-67 164
Abstract
We prove that any virtual knot can be presented as a connected sum of several prime and trivial virtual knots. Prime summands of the presentation are defined uniquely, i.e. they are determined by the original knot. We introduce two types of reductions on the set of knots in thickened surfaces and prove that the result of any sequence of reductions exists and is defined uniquely.
67-72 153
Abstract
It is well known that any knot in S3 can be represented as a connected sum of prime summands. Moreover, the summands are determined uniquely. This is the famous theorem of H. Schubert (1949). Is a similar result true for knots in thickened surfaces, that is, in 3-manifolds of the type F х I, where F is a closed orientable surface? It turns out that the existence theorem is true but the uniqueness theorem is false (there are counterexamples). In the paper we describe the general structure ofall possible counterexamples.
73-81 169
Abstract
We extend the concept of diagrams and associated Reidemeister moves for links in S3 to links in lens spaces, using a differential approach. As a particular case, we obtain diagrams and Reidemeister type moves for links in RP3 introduced by Y.V. Drobothukina.
82-87 196
Abstract
The t-invariant of 3-manifolds is an essential part of the Turaev-Viro invariant corresponding to the 5-th root of unity. Sapphire manifolds are result of pasting two orientable thickened Klein bottles along their boundaries. The manifold is defined by a 2 x 2 matrix of the pasting. A formula for values of the t-invariant is given in the work. The formula is a function on the matrix four elements.
87-92 153
Abstract
We prove a formula for an upper bound of complexity of graph-manifolds obtained by gluing together two Seifert manifolds fibered over the disc with two exceptional fibers.
93-105 157
Abstract
The brief overview of Riemannian special holonomy groups is given in the paper. Explicit constructions of Spin(7)- and G2-holonomy metrics are described.
106-118 187
Abstract
By means of binary and ternary number systems, the authors solve two problems: the search of finite collections of weights with any given total weight m € N (kg), in particular with minimal number of weights, such that one can weigh a load of any weight n € N П [1,m] (kg), using one-sided or two-sided placement of weights; a coordinate description of Sierpinski gasket and carpet, Menger sponge. On the ground of solution of the second problem, it is proved that restriction of the Euclidean metric to any of these three sets and inner metric, induced by this restriction, are bi-Lipschitz equivalent. It is given a direct proof of known fact that Hausdorff dimensions of all these sets coincide with their fractal dim
119-133 196
Abstract
This paper is devoted to the theory of the invariant tensor fields on Lie groups which is one of the sections of modern Riemannian geometry. It is proposed to give a short survey of some results this theory which is similar to the other studies conducted by the authors.
134-139 184
Abstract
The space Z of leftinvariant orthogonal almost complex structures on 6-dimensional Lie groups is researched. For the explicit view of this space elements the isomorphism of Z and CP3 is used. Representation of CP3/T3 as 3-dimensional tetrahedron is used too. The explicit formula for almost complex structure as composition ofrotations is found.
139-142 186
Abstract
A new class of smoothing spline cubic curves is considered in the article.These curves are neither в-spline curves not Bezier curves.The parametric equations of the curves are obtained and some geometric properties ofthis curves are studied.
142-146 187
Abstract
This work introduces the special class of almost complex structures which provide the tangent space decomposition into direct sum of the vector subspaces, and invariant act on these subspaces. Some concepts and results are provided For such almost complex structures on the homogeneous
147-150 197
Abstract
We introduce equation of a flow for the Spin(7)-structure on a cone over 7-dimensional 3-Sasakian manifold.
151-154 185
Abstract
With use of procedures of symbolic computations on Maple the Lie algebras of dimension 5 supposing left invariant semi-Riemannian K-contact-Sasaki-Einstein structures are found. On one of Lie algebras of dimension 5 as an example the family of Sasaki structures is found in the obvious form and geometrical properties of metrics of family are received.
155-168 152
Abstract
Left-invariant pseudo-Kahler structures on the six-dimensional nilpotent Lie groups, depending only from those parametres which influence curvature are discovered. All such structures have a zero Ricci tensor, Pseudo-Riemannian norm and the majority of them are not flat. The received pseudo-Kahler structures give simple models pseudo-Kaahler six-dimensional nilmanifolds
168-181 190
Abstract
A Riemann-Cartan manifold is a triple (M,g, V), where (M,g) is a Riemannian n-dimensional (n > 2) manifold with linear connection V having nonzero torsion S such that Vg = 0. We consider properties of pseudo-Killing and pseudo-garmonic vector fields on some classes of these manifolds and vanishes theorems as corollaries of these properties
181-186 107
Abstract
In N(k)-contact metric manifolds and/or (k, /л)-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with V pointwise collinear with the structure vector field £ are
186-192 150
Abstract
In this paper we study the set of integral curves completely parallelizable Pfaffian system. It is shown that this set is a Banach manifold
193-199 153
Abstract
The theory of multiplicative functions and Prym differentials on a compact Riemann surface has found numerous applications in function theory, analytic number theory and equations of mathematical physics [1¬4]- The work purpose - to receive new properties of meromorphic Prym differentials and abelians differentials on variable compact Riemann surfaces and variable character, in connection with divisors-
199-202 172
Abstract
In the present paper we give the description of the set of convergence for Mellin-Barnes integral representing solution to the general algebraic equation.
203-205 145
Abstract
It is obtained the Poincare-Bertrand formula for singular Cauchy-Szego integral in a multidimensional ball. It is considered principal value of integral in terms of Cauchy and in terms of Kerzman-Stein. The received formula in case of consideration of a Cauchy principal value differs from Poincare-Bertrand formula for Cauchy integral in a complex plane. However, in case of consideration of a principal value in terms of Kerzman-Stein the received formula of change of integration order is coincide with Poincare-Bertrand formula. This paper is a review of the main results on this problem.
206-211 164
Abstract
The theory of multiplicative functions and Prym differentials on torus has found applications in the theory of functions, the analytical theory of numbers and in the equations of mathematical physics [1-7]. The work purpose - to receive new properties of meromorphic Prym differentials and abelians differentials on variable torus and variable characters, in connection with divisors.
211-216 206
Abstract
Harmonic Prym differentials and their periods classes play the big role in contemporary theory functions on compact Riemann surfaces. In this paper is investigated harmonic Prym bundle, whose fibre is space of harmonic Prym differentials on variable compact Riemann surfaces. Proven that cohomology Gunning bundle, which connect with periods classes, are real analytically isomorphic harmonic Prym bundle over product Teichmueller space and a space of nontrivial normalized characters.
216-223 159
Abstract
In spaces of multiplicative meromorphic automorphic forms the integral norm, bilinear pairing and the integral Bers operator for any character are entered. Under study an universal estimation of norm, selfadjointness for Bers operator in case of meromorphic (q, р) - forms and an analog of an inequality of Schwarz are received.
224-238 141
Abstract
The theory of multiplicative functions and Prym differentials for case special characters on a compact Riemann surface has found numerous applications in geometrical theory function complex variable, analytic number theory and equations of mathematical physics [1-9]. In [8] is begun construction a general theory of multiplicative functions and Prym differentials on a compact Riemann surface for arbitrary characters. In this survey is represented results on theory of multiplicative functions and Prym differentials on a variable compact Riemann surfaces of genus g > 1, which obtained in papers V.V. Chueshev, M.I. Golovina and T.A. Pushkareva. There are analogous results for Prym differentials on torus (T.S. Krepizina) and on finite Riemann surfaces (A.A. Kazanzeva). These three cases essentially differ from each other and by results, and by methods.
239-243 185
Abstract
The work is devoted to the calculus of differential forms of Sobolev type. The authors of [2, 3] investigated a situation similar to the embedding theorem of Sobolev space W} into the space of continuous functions provided p > n, defined Jx и and established the Stokes' theorem jx uu = du. In this paper we study the case corresponding to the embedding of W}, into the Lq provided p < n. In this case we give meaning to the integral of k-forms on k-dimensional oriented manifold, to be consistent with already existing theory. We set the Stokes' formula Jx и = du in the model case of X С К", dimX = n. The existence of the integral in the right hand side is understood in the sense described in this paper.
243-249 149
Abstract
We describe the group of С2-smooth isometries on contact sub-Riemannian manifold, precisely on roto-translation group. We find the conditions providing for a vector field to generate the local one-parameter group of contact or local biLipschitz transformations of roto-translation group.
250-254 208
Abstract
Mean ergodic theorem convergence rate inequalities are obtained. The existence of such inequalities is implied by the equivalence between power-function convergence rate in this theorem and the presence of the power singularity (with the same exponent) of averaging function spectral measure at zero which is related with corresponding dynamical system. The same convergence rate was also estimated via correlation coefficients. Important for possible applications particular cases when correlation coefficients decay rate is power and exponential were considered apart. Estimates for pointwise ergodic theorem convergence rate were obtained for the case when mean ergodic theorem convergence rate is known. All results of the paper have their exact analogues for stationary in the wide sense stochastic processes.
255-258 150
Abstract
We obtain exponential estimates of the rate of convergence in Birkhoff and Bowen theorems for uniformly hyperbolic systems. Well-known analogous estimates for large deviations in these theorems, are used in the proof.
258-263 207
Abstract
Spectral analysis of signals is An important applied problem, in particular the allocation of the periodic component. The classical approach to this task solution - Fourier Analysis and its various modifications (such as wavelet analysis). Fourier analysis is best suited for the study of signals under consideration for the entire time axis. The finite signals are defined on a finite interval with the "artificial" must be replaced at no limited. In this paper, a direct variational method for studying finite signals in Lebesgue spaces L2 [a, b] and more generally in the Sobolev spaces Wp[a,b] . Located in the best sense of the norms of these spaces, the periodic component. For finite digital signals, the algorithm is implemented in the MatLab.
263-266 204
Abstract
Investigation solvability boundary value problem for differential equation fourth order be occupied with many mathematicians in Russia and in abroad. This paper devoted investigation five boundary value problems for one equation fourth order. Regular solution one boundary value problem for differential equation with partial derivative fourth order exist and uniquely. Examples non stability solutions for three other boundary value problem for this equation are constructed. Example solution one boundary value problem for this equation is constructed, such that under condition analyticity coeffificients and analytic on the right-hand side given equation, but solution is not belong Sobolev's space H4,1(D).
266-268 195
Abstract
Investigation solvability boundary value problem for differential equation fourth order be occupied with many mathematicians in Russia and in abroad. This paper devoted investigation three boundary value problem for one equation fourth order. Regular solution one boundary value problem for differential equation with partial derivative fourth order exist and uniquely. Constructed examples non uniquely solutions for two other boundary value problem for this equation.
269-274 198
Abstract
The problem on determination of the upper and lower Riesz bounds for the m-th order B-spline basis is reduced to analysis of the series Т.7=-оо (x-j)2m . It is shown that the sum of the series is a ratio of certain trigonometric polynomials. Some properties of these polynomials which help to determine the Riesz bounds are established. The results
275-288 188
Abstract
This article contains a short review of the theory of functional classes of Sobolev type defined on a metric space (X,d), equipped with a Borel measure More detailed discussion of Banach function spaces Mp)(X,d, introduced by P. Hajlasz, and related classes of mappings.
288-292 167
Abstract
For exponential small solution singular perturbation Diroichlet's problem global formal asymptotic expansion are constructed by means offunction ofboundary layer type
ISSN 2949-2122 (Print)
ISSN 2949-2092 (Online)
ISSN 2949-2092 (Online)
