Issue 1, Volume 31, April 2006

2006 · Open access

1. REVERSES OF THE CAUCHY-BUNYAKOVSKY-SCHWARZ AND HEISENBERG INTEGRAL INEQUALITIES FOR VECTOR-VALUED FUNCTIONS IN HILBERT SPACES S. S. DRAGOMIR PDF

   ▸ Abstract

   Some reverses of the Cauchy-Bunyakovsky-Schwarz integral inequality for vector-valued functions in Hilbert spaces and applications for the Heisenberg inequality are provided.

   1-15
2. ON MAXIMALITY FOR SOME KINDS OF CODES OVER TWO-LETTER ALPHABETS KIEU VAN HUNG PDF

   ▸ Abstract

   Superinfix codes, p-superinfix codes and s-superinfix codes have been introduced and considered by D. L. Van, P. T. Huy and the author in earlier papers. The embedding problem for these classes of codes has been proved to have positive solution in both the finite and regular case. Also, these kinds of codes can be characterized by means of variants of Parikh vectors. In this paper we consider these codes in the case of two-letter alphabets. Based on the mentioned above vector characterizations, it is shown that, for each of the classes of codes under consideration, there exists a procedure to generate all finite maximal codes in the class, starting from anyone among them. Embedding algorithms, other than those obtained earlier, for these classes of codes are also exhibited.

   17-30
3. ON THE ASYMPTOTIC EQUIVALENCE OF LINEAR DELAY EQUATIONS IN BANACH SPACE DANG DINH CHAU PDF

   ▸ Abstract

   In this paper we present some sufficient conditions for the asymptotic equivalence of linear evolution equations with time-delay in Banach spaces. Besides, we discuss the asymptotic relationship between $C_0$ groups and strongly continuous evolutionary processes. The obtained results extend the Levinsons theorem on the asymptotic equivalence of linear differential equations.

   31-38
4. THE BERTRAND OFFSETS OF RULED SURFACES IN $\mathbb R^3_1$ E. KASAP , N. KURUOGLU PDF

   ▸ Abstract

   The problem of finding a curve whose principal normals are also the principal normals of another curve was apparently first proposed by Saint-Venant but solved by J. Bertrand. Such curves were referred to as ‘Bertrand offsets’. In this paper, a generalization of the theory of Bertrand curves is presented for ruled surfaces in Minkowski space $\mathbb R^3_1$. Using lines instead of points, two ruled surfaces which are offset in the sense of Bertrand are defined. The obtained results are illustrated by computer-aided examples.

   39-48
5. SOME REMARKS ON STABILITY IN PERIODIC MULTI-WAVELET DECOMPOSITIONS DINH DUNG, VU CONG BANG PDF

   ▸ Abstract

   In the present paper, we established some necessary and sufficient conditions for $L_p$-stability of periodic multi-wavelet decompositions.

   49-59
6. MIXED MULTIPLICITIES OF IDEALS AND OF REES ALGEBRAS ASSOCIATED WITH RATIONAL NORMAL CURVES NGUYEN DUC HOANG PDF

   61-75
7. SOME ALGORITHMS FOR SOLVING MIXED VARIATIONAL INEQUALITIES TRUONG QUANG BAO, PHAN QUOC KHANH PDF

   ▸ Abstract

   We propose some algorithms for solving mixed variational inequalities. The global convergence of these algorithms is established under pseudomonotonicity and continuity assumptions without Lipschitz conditions. The implementation is illustrated on a nonsmooth optimization test problem.

   77-98