The 6j-Symbols for the SL(2, ℂ) Group

Theoretical and Mathematical Physics - We study 6j-symbols or Racah coefficients for the tensor products of infinite-dimensional unitary principal series representations of the group SL(2,...     

A New Class of Completely Unitary Invariants in B_n(Ω) and the Commutant of Weighted Unilateral Shift Operators

ＡＮｅｗＣｌａｓｓｏｆＣｏｍｐｌｅｔｅｌｙＵｎｉｔａｒｙＩｎｖａｒｉａｎｔｓｉｎＢ_ｎ（Ω）ａｎｄｔｈｅＣｏｍｍｕｔａｎｔｏｆＷｅｉｇｈｔｅｄＵｎｉｌａｔｅｒａｌＳｈｉｆｔＯｐｅｒａｔｏｒｓＹａｎＣｏｎｇｑｕａｎ（严从荃）（ＤｅｐａｒｔｍｅｎｔｏｆＭ?..     

Calculating the Fundamental Group of Galois Cover of the(2, 3)-embedding of CP~1× T

As known to all,it is quite difficult to compute the fundamental group of a surface of general type.In this paper,applying Moishezon-Teicher's algorithm,we investigate the fundamental group of a special surface of general type with zero topological index,namely,the Galois cover of the(2,3)-embedding of CP~1×T.Because the full presentation of the group is very complicated,we compute its special quotient and get an interesting result about its structure.     

On the Porosity of the Limit Set and the Boundedness of Oscillation for the Function log(dist(x,Λ))in the Case of a Fuchsian Group without Parabolic Elements

Let be the limit set of a finitely generated Fuchsian group of the second kind. If the group does not contain parabolic elements, then is porous and the function belongs to the class BMO. Bibliography: 2 titles.     

Operational Calculus for the Fourier Transform on the Group GL(2,ℝ) and the Problem about the Action of an Overalgebra in the Plancherel Decomposition

The Fourier transform on the group GL(2,?) of real 2 × 2 matrices is considered. It is shown that the Fourier images of polynomial differential operators on GL(2,?) are differentialdifference operators with coefficients meromorphic in the parameters of representations. Expressions for operators contain shifts in the imaginary direction with respect to the integration contour in the Plancherel formula. Explicit formulas for the images of partial derivations and multiplications by coordinates are presented.     

Estimate of the norm ∥f(A1, A2)-f(B1, B2)∥ for pairs of self-adjoint commuting operators

In this note we announce the estimate for the difference mentioned in the title, where are the lengths of intervals containing the spectra of the operators A₁, B₂ and A₂, B₂; the function f is from the class Lip 1 (with constant 1). The outline of the proof of this estimate is given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 175–177, 1984.     

A new proof of the existence of (q 2−q+1)-arcs inPG(2,q 2)

Journal of Geometry -     

On the Evaluation of the Tutte Polynomial at the Points (1, –1) and (2, –1)

Motivated by the identity t (K _n+2; 1, –1) = t (K _n ; 2, –1), where t(G; x, y) is the Tutte polynomial of a graph G, we search for graphs G having the property that there is a pair of vertices u, v such that t(G; 1, –1) = t(G – {u, v}; 2, –1). Our main result gives a sufficient condition for a graph to have this property; moreover, it describes the graphs for which the property still holds when each vertex is replaced by a clique or a coclique of arbitrary order. In particular, we show that the property holds for the class of threshold graphs, a well-studied class of perfect graphs.     

A necessary and sufficient condition for the biorthogonality of {ρ 1,ρ 2}

In this paper, we present a necessary and sufficient condition for the biorthogonality of a class of special functionsρ ₁ andρ ₂. The functions are useful in the theory of biorthogonal wavelet.     

A conjecture of Abe-Iiyori and the Ree groups ~2F_4(q),Ⅱ

In this paper the author has solved a problem of Abe and liyori for the finite simple groups 2F4(q) and 2F4(2)'.     

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅱ)——Also on the unity of the Continuous Induction,the Mathem atical Induction and the Transfinite Induction

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＣｏｎｔｉｎｕｏｕｓＩｎｄｕｃｔｉｏｎｏｆｒｅａｌｎｕｍｂｅｒｉｓｒｅｗｒｉｔｔｅｎａｓｂｅｌｏｗｉｎｔｈｉｓｐａｐｅｒ（Ⅰ）．ＴｈｅＣｏｎｔｉｎｕｏｕｓＩｎｄｕｃｔｉｏｎ（Ａ）：ＳｕｐｐｏｓｅｔｈａｔＰｘｉｓａｐｒｏｐｏｓｉｔｉｏｎｃｏｎｃｅｒｎｉｎｇａｒｅａｌｎｕｍｂｅｒｘ．Ｉｆｔｈｅｒｅｉｓｓｏｍｅｘ０ｓｕｃｈｔｈａｔＰｘｉｓｔｒｕｅｆｏｒｅｖｅｒｙｘ＜ｘ０，ｔｈｅｎＰｘｉｓｔｒｕｅｆｏｒｅｖｅｒｙｒｅａｌｎｕｍｂｅｒｘ．ＩｆＰｘｉｓｔｒｕｅｆｏｒｅ…     

Isomorphism of the Yangian Yħ(A(m,n)) of the Special Linear Lie Superalgebra and the Quantum Loop Superalgebra Uħ(LA(m,n))

Theoretical and Mathematical Physics - Using the approach of Gautam and Toledano Laredo, we construct an explicit isomorphism of the Yangian Y?(A(m, n)) of the special linear Lie superalgebra...     

On the Scientific,Pedagogic, and Public Activities of Academician Mikhail Alekseevich Lavrent'ev at the Ukrainian Academy of Sciences (1939–1949) (on the 100th Anniversary of the Birth of M. A. Lavrent'ev)

Ukrainian Mathematical Journal -