IN this paper we are concerned with the problem of classifying compact surfaces immersed in Iw” up to regular homotopyt. This subject started in 1958 when Smale classified the immersions of the 2-sphere [17]. For n 2 4 the problem was then completely solved by Hirsch ([8], theorems 8.2 and 8.4): if M2 is a compact surface then for n 2 5 any two immersions f, g : M2 + R” are regularly homotopic,...

A graph G is called integral or Laplacian integral if all the eigenvalues of the adjacency matrix A(G) or the Laplacian matrix Lap(G) = D(G)−A(G) of G are integers, where D(G) denote the diagonal matrix of the vertex degrees of G. Let Kn,n+1 ≡ Kn+1,n and K1,p[(p−1)Kp] denote the (n+1)-regular graph with 4n+2 vertices and the p-regular graph with p2 + 1 vertices, respectively. In this paper, we ...

conclusions reasons associated with initial and continued co-use of heroin kerack with ma, factors associated with treatment entry and the differences between regular and recreational co-users should be specifically considered in designing and tailoring drug use treatment programs for this group. materials and methods 82 clients were randomly recruited. a researcher-designed questionnaire was u...

— The main purpose of this note is to collect a number ofscattered properties, examples and unanswered questions concerning classes of languages which are proof against varions farms of pumping of the words in the language. These forms of pumping lead to different infinité hiérarchies. Requiring that it must be possible to select from a prefix the substring to be repeated independently of the s...

We assign to each positive variety V and a fixed natural number k the class of all (positive) boolean combinations of the restricted polynomials, i.e. the languages of the form L0a1L1a2 . . . a`L`, where ` ≤ k, a1, . . . , a` are letters and L0, . . . , L` are from the variety V. For this polynomial operator we give a certain algebraic counterpart which works with identities satisfied by syntac...

Muslims believe that the The Holy Quran is the message of God Almighty which has been transmitted to His messenger, Prophet Mohammad (PBUH), through revelation in the Arabic language. This Holy book has been translated into many languages, including English. Although the content of the The Holy Quran has been translated into the English language, few studies have been conducted to explore the b...

Muslims believe that the The Holy Quran is the message of God Almighty which has been transmitted to His messenger, Prophet Mohammad (PBUH), through revelation in the Arabic language. This Holy book has been translated into many languages, including English. Although the content of the The Holy Quran has been translated into the English language, few studies have been conducted to explore the b...

We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...