CYCCYCLIC VECTORS AND CELLULAR INDECOMPOSABLE OPERATORS ON Q_p SPACES

We identify the functions whose polynomial multiples are weak＊ dense in Qp spaces and prove that if ｜f（z）｜ ≥ ｜g（z）｜ and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mx on Qp spaces is cellular indecomposable.

Indecomposable Representations of the Square—Root Lie Algebras of Vector Type and Their Boson Realizations

The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.

EXPLICIT DESCRIPTION OF A CLASS OF INDECOMPOSABLE INJECTIVE MODULES

Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.

Two Dimensional Indecomposable Modules over Infinite Dimensional Hereditary Path Algebras

Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.

The Spectrum of Linear Operators on Quotient Indecomposable Banach Spaces

This paper discusses the special properties of the spectrum of linear operators （in particular, bounded linear operators） on quotient indecomposable Banach spaces; shows that in such spaces generators of C0-groups are always bounded linear operators, and that generators of C0-semigroups satisfy the spectral mapping theorem; and gives an example to show that the generators of C0-semigroups in quotient indecomposable spaces are not necessarily bounded.

Some Characterizations of Hereditarily Indecomposable Banach Spaces

In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces.

Annihilator Ideals of Indecomposable Modules of Finite-Dimensional Pointed Hopf Algebras of Rank One

Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed feld of characteristic zero.We describe all annihilator ideals of indecomposable H-modules by generators.In particular,we give the classification of all ideals of the finite-dimensional pointed rank one Hopf algebra of nilpotent type over the Klein 4-group.

Further study on indecomposable cryptographic functions

1 Introduction Boolean functions have important applications in stream ciphers and block ciphers.Over the last decades,the constructions of cryptographic Boolean functions have paid a lot of attention[1,2].Direct sum is a well-known secondary construction of cryptographic functions[3].By using the direct sum,a lot of functions with high nonlinearities can be obtained[4,5].However,the direct sum of two functions are decomposable functions,which have numerous null secondorder derivatives(which represents a potential weakness with respect to the higher order differential attack)[6].(In)decomposable functions were also studied in[7]by Zheng and Zhang under the name(non)separable functions.They provided some sufficient conditions that the functions are indecomposable[7].

Projective and indecomposable S-acts

LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss S and is closed under coproducts and summands. It is proved that, inC, anS-actP is projective and unitary if and only ifP? ? j? I Se i ,e i ?E. In particular,P is a projective, indecomposable and unitary object if and only ifP ?Se for somee ∈E. These generalize some results obtained by Knauer and Talwar.

CONSTRUCTION OF INDECOMPOSABLEDEFINITE HERMITIAN FORMS

This Paper gives a method to construct indecomposable positive definite integral Hermitianforman imnginary quadratic field Q with gin discriminant and g。n rank.It is shown that for ally natural numbers n and a, there are n-ary Indecomposable positivedefinite intopal Herlllltian lattices over Q(resp. Q)with discriminant a, exceptfor four(resp. one) exceptions. In these exceptional cases there are no lattices with the desiredproperties.

λ-fold indecomposable large sets of Steiner triple systems

A family (X, B1), (X, B2), . . . , (X, Bq) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTSλ(v) if there exists no LSTSλ (v) contained in the collection for any λ 【 λ. In 1995, Griggs and Rosa posed a problem: For which values of λ 】 1 and orders v ≡ 1, 3 (mod 6) do there exist IDLSTSλ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v) (HLSTSλ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ = 2, 3, 4 and v ≡ 1, 3 (mod 6).

Indecomposable Calabi-Yau Objects in Stable Module Categories of Finite Type

The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective algebras with such properties, the ones whose stable categories are not Calabi-Yau are determined. For the remaining ones, i.e., those selfinjective algebras whose stable categories are actually Calabi-Yau, the difference between the Calabi-Yau dimensions of the indecomposable Calabi-Yau objects and the Calabi-Yau dimensions of the stable categories is described.

On Indecomposable Definite Hermitian Forms

In this paper, for any given natural numbers n and a, we can construct explicitly positive definite indecomposable integral Hermitian forms of rank n over Q(-31/2) with discriminant a, with the following ten exceptions: n=2, a=1,2,4, 10; n=3, a=1,2,5; n=4, a=1; n=5, a=1; and n=7, a=1. In the exceptional cases there are no forms with the desired properties. The method given here can be applied to solving the problem of constructing indecomposable positive definite Hermitian Rm-lattices of any given rank n and discriminant a, where Rm is the ring of algebraic integers in an imaginary quadratic field Q(-m1/2) with class number unity.

On Hereditarily Indecomposable Banach Spaces

This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.

Construction of indecomposable definite Hermitian forms

Let F=Q(-m1/2) （m】0 and square-free） be an imaginary quadratic field and Dm the ring of algebraic integers in F. The field F has a unique non-trivial involution （the complex conjugation） whose fixed field is Q. Let V be an n-dimensional non-degenerate Hermitian space over F equipped with a sesquilinear form φ on Ⅴ with respect to the involution and Hermitian form H associated with φ. Let L be a Dm-lattice on V, i.e. a finitely generated Dm-module in Ⅴ and FL=V. L is called even lattice if H（x）∈2Z for any x∈L; otherwise, it is odd. L is indecomposable if it cannot be expressed as an orthogonal sum of two non-zero sublattices; in other words, L=P （?） R implies P=0 or R=0. The minimum of a Hermitian Dm-lattice L With respect to its associated Hermitian form h

On Indecomposable Positive Definite Integral Hermitian Forms

Let F=Q(i=m1/2（i2=-1, m】0 and square free） be an imaginary quadratic field and Rm its ring of algebraic integers. The aim of this note is to construct n-ary positive definite indecomposable integral. Hermitian forms over Rm with given rank and given discriminant. The word decomposition or splitting is the geometric one, i. e. lattice L has a non-trivial expression of the form L=M⊥N. If there is no such expression we call L indecomposable. There is another kind of decomposition——a more algebraic one. A positive definite Hermitian

LOEWY FACTORS OF INDECOMPOSABLE MODULES OVER SELF-INJECTIVE ALGEBRAS OF CLASS AN

This paper proves that every indecomposable module over a representation-finite selfinjective algebra of class An is uniquely determined by its Loewy factors and every indecomposable module is multiplicity-free. As an application to the representation theory of finite groups, it is obtained that every indecomposable module over blocks with cycle defect groups is uniquely determined by its Loewy factors and every indecomposable module is multiplicity-free.

A conjecture about the strict fully indecomposable exponents of primitive matrices

The conjecture about the strict fully indecomposable exponents of nxn primitive Boolean matrices are proved as follows:

CONSTRUCTION OF INDECOMPOSABLE POSITIVE DEFINITE UNIMODULAR HERMITIAN FORMS

This paper gives a method to construct indecomposable positive definite unimodular Hermitian (?)-lattices of any rank n with m(?)3 (mod 4). It is proved that we can construct: (i) for any natural number n, an indecomposable positive definite normal unimodular (?)-(resp. (?)-lattice of rank n, except n=2, 3, 4,5 (resp. n=2, 3) (in the exceptional cases there are no lattices with the desired properties), and (ⅱ) for any n=4k(resp. n=2k), an indecompoaable positive definite even unimodular (?) lattice of rank n.

Indecomposable representations of the Lie algebra of derivations for d-torus

Let DerA be the Lie algebra of derivations of the d-torus A = C[t1± 1, . . . , td±1]. By applying Shen-Larsson’s functors we get a class of indecomposable DerA-modules from finite-dimensional indecomposable gld-modules. We also give a complete description of the submodules of these indecomposable DerA-modules. Our results generalize those obtained by Rao.