The mitochondrion of sea urchin sperm is located at the base of the sperm head, and the flagellum extends from the mitochondrion for approximately 40 microM. These sperm have two known flagellar, non-mitochondrial, enzymatic systems to rephosphorylate ADP. The first involves the phosphocreatine shuttle, where flagellar creatine kinase (Sp-CK) uses phosphocreatine to rephosphorylate ADP. The sec...

and Applied Analysis 3 Generalized derivations first appeared in the context of operator algebras 7 . Later, these were introduced in the framework of pure algebra 8, 9 . Definition 1.1. LetA be an algebra and let X be anA-bimodule. A linear mapping d : A → X is called i derivation if d ab d a b ad b , for all a, b ∈ A; ii generalized derivation if there exists a derivation in the usual sense δ...

Example 3. For k′/k a finite separable extension and H any linear algebraic k-group, we have H ↪−→ Rk′/k(Hk′) =: H ′, where Rk′/k(Hk′) is the Weil restriction functor (which is representable by a linear algebraic k-group). This functor is defined by Rk′/k(Hk′)(A) = Hk′(A⊗k k′), so the injection H ↪−→ Rk′/k(Hk′) is given by sending a k-morphism SpecA→ H to its base change by k′. Then we have [H ...

This paper shows that for a given irreducible representation ρ of Γ/Γ1, the two functions dim(Mk(Γ1, ρ)) and dim(Sk(Γ1, ρ)) of k are almost linear functions. Let Γ and Γ1 be two Fuchsian subgroups of SL2(Q) of the first kind, with Γ1 a normal subgroup of Γ of index μ. Let H denote the extended upper half-plane [4] and put Y = Γ\H and X = Γ1\H . Let Ak(∗) denotes the space of meromorphic modular...

Given a real matrix A ∈ Rm×n of rank r, and an integer k < r, the sum of the outer products of top k singular vectors scaled by the corresponding singular values provide the best rank-k approximation Ak to A. When the columns of A have specific meaning, it might be desirable to find good approximations to Ak which use a small number of columns of A. This paper provides a simple greedy algorithm...

Let (Ω,F , P ) be a probability space. For each G ⊂ F , define G as the σ-field generated by G and those sets F ∈ F satisfying P (F ) ∈ {0, 1}. Conditions for P to be atomic on ∩i=1Ai, with A1, . . . ,Ak ⊂ F sub-σ-fields, are given. Conditions for P to be 0-1-valued on ∩i=1Ai are given as well. These conditions are useful in various fields, including Gibbs sampling, iterated conditional expecta...

We study the problem of adsorption and collapse transition of a linear polymer chain situated in a fractal container represented by a 4-simplex lattice and interacting with a surface adsorbed linear polymer chain. The adsorbed chain monomers act as pinning sites for the polymer chain. This problem has been solved exactly using real space renormalization group transformation. The resulting phase...

Let Ak = {0 = a1 < a2 < ... < ak} and B = {0 = b1 < b2 < ... < bn ...} be sets of k integers and infinitely many integers, respectively. Suppose B has asymptotic density x t d(B) x. If, for every integer n _> 0, there is at most one representation n a^ + bj , then we say that Ak has a packing complement of density j> x. Given Ak and x9 there is no known algorithm for determining whether or not ...

OBJECTIVE Actinic keratoses (AK) are proliferation of neoplastic keratinocytes confined to the epidermis induced by damaging solar ultraviolet radiation (UVR). When the neoplastic keratinocytes extend in to papillary-reticular dermis, then the lesion termed as squamous cell carcinoma (SCC). We have compared HLA class I and II antigen profiles in three patient groups namely: AK (n: 31) (patients...

The main aim of this paper is to prove a bilateral inequality for P [‖ n ∑ 1 akrk‖ > t ] , where t > 0, (ak) are elements of a normed space, while (rk) are Rademacher functions. Then this inequality is applied for estimation of E‖ n ∑ 1 akrk‖. As another corollary we give a maximal inequality for exchangeable random variables that recently has been published in [4]. 2000 Mathematics Subject Cla...