Abstract: Abstract In a pre-industrial agrarian society in which families and households were the primary unit of production as well as consumption, households responded differently to short-term economic stress, depending on the resources available and other household conditions. Furthermore, like most enduring human groups, families and households were never entirely egalitarian, and individual members’ well-being and chances of survival were affected by the structure of their household and their position within that structure.

Abstract: This chapter has sections titled: Introduction Description Strengths Weaknesses Particular applications The future References

Abstract: Let A be an f-algebra with unit and L,M be two f-modules on A. We define f-orthomorphisms from L into M and show that these operators coincide with the f-linear operators whenever M is topologically full with respect to A. We show that f-orthomorphisms enjoy many of the properties of orthomorphisms.

Abstract: In this paper,we investigate power-substitution over exchange rings.We show that an exchange ring R satisfies power-substitution if and only if for any regular x ∈ R, there exists a positive integer n such that xI n is unit πregular in M n(R).

Abstract: If G is an ordered abelian group with a generating order unit u, the order interval G+ [0, u]:={p ∈ G|0 ≤ p ≤ u} can be given the structure of an effect algebra in a natural way. Conversely, most effect algebras that arise in practice are interval effect algebras, i.e., are isomorphic to effect algebras of the form G+ [0, u]. The pair (G, u) is called a unigroup iff every abelian group-valued measure on the interval effect-algebra G+ [0, u] lifts to a (necessarily, unique) group homomorphism on G. An interval effect algebra has, up to isomophism, a unique representation as the order interval of a unigroup. Thus, a great part of the theory of effect algebras (and thus, of algebraic quantum logic) can be recast as a chapter of the theory of ordered abelian groups. In particular, the study of group actions on interval effect algebras amounts to the study of representations of groups on unigroups.

Abstract: Abstract Patients who wear pajamas, and see hospital garb around them think of themselves as sick. If they and their caretakers wear street clothes, patients will think of themselves as moving out of the sick role, and into rehabilitation. They will be ready for life outside the hospital. This is the rehab philosophy, and this is what makes this unit unique.

Abstract: Abstract Over the past twenty years or so applied macroeconomics has been transformed by the widespread adoption of a set of new statistical techniques. The techniques I shall focus on are: unit-root tests, vector autoregressions (VARs), Granger-causality tests, and cointegration, which I will refer to as ‘unit roots etc.’. Although these techniques were invented to answer statistical questions, they diffused very rapidly through applied economics because they were thought to be able to answer important theoretical questions in macroeconomics.

Abstract: Let Abe an Archimedean uniformly complete f-algebra with unit element. It is proved that the following conditions are equivalent:(1) Ais semi-hereditary; (2) Ais coherent; (3) Ais projectable; (4) Ais Dedekind σ-complete.

Abstract: In this paper,the concept of fuzzy homomorphism of rings h as been introduced,and a theorem homomorphism concerning λ of rings a nd a fundamental theorem homomorphism of rings (having unit) have been establish ed.Some of its properties are also discussed.

Abstract: In this paper, we consider hyperstructures (H, ·) whenH = {e, a, b} We put a condition on (H, ·) wheree is a unit We obtain minimal and maximalH v-groups, semigroups and quasigroups, using Mathematica 30 computer programs

Abstract: Describes a three-week project in an English classroom in which students in small, mixed-ability groups used PowerPoint to enhance a unit on British literature. Outlines the lesson itself and discusses its positive results, including peer-teaching and learning, improved student motivation to understand themes in poetry, positive socialization, and learning to be a team player. Notes further teaching ideas integrating technology.

Abstract: Abstract Once an innovation is created and developed (either within or outside of an organization), how should it be introduced and implemented by an adopting organization? in particular, if management has made the strategic choice to adopt an administrative innovation throughout its organization, should management begin by concentrating its implementation efforts in depth in one or two specific organizational subunits, or in breadth across all organizational subunits? The first approach, which we will call a depth adoption strategy, assumes that after an innovation has been successfully adopted and debugged by a demonstration unit, it can be transferred and diffused to other organizational units. The second approach, called a breadth adoption strategy, assumes that a more effective way to change an organization is to introduce and implement an innovation across the board, often through successive hierarchical levels across all organizational units.

Abstract: We give two theorems on the existence of the unit in commutative Banach algebras. As corollaries, we obtain results of V. Runde and P. G. Dixon.

Abstract: We show that if R is an exchange ring, then the following are equivalent: (1) R satisfies related comparability. (2) Given a, b, d ∈ R with aR + bR = dR, there exists a related unit w ∈ R such that a + bt = dw. (3) Given a, b ∈ R with aR = bR, there exists a related unit w ∈ R such that a = bw. Moreover, we investigate the dual problems for rings which are quasi-injective as right modules.

Abstract: The title compound, 3,3a,5,5a,6,7,8,9-octahydro-3a-hydroxy-5a-methyl-8-(2-prop­enyl)­furo­[3,2-c]­iso­benzo­furan-2-one, C14H20O4, crystallizes with two independent molecules in the asymmetric unit. The molecules have similar metric parameters but differ in the conformations of the isopropenyl groups. The hydroxyl groups form one-dimensional chains of hydrogen bonds.

Abstract: Consider the multiplicative semigroup M (S)of all probability distribution fu ctions on subsets S of R 2 .This structure corresponds to the coordi atewise maximum of S -valued independe t random vectors. We provide a wide class of possible territories S, where in spite of the lack of the u it element in M (S),there is a Khinchine-type decomposition.I case M (S)has a unit element,we characterize the subsets S with the property that there is a decompositio in M (S).

Abstract: We establish a duality between two categories, extending the Stone duality between totally disconnected compact Hausdorff spaces (Stone spaces) and Boolean rings with a unit. The first category denoted by RHQS, has as objects the representations of Hansdorff quotients of Stone spaces and as morphisms all compatible continuous functions. The second category, denoted by BRLR, has as objects all Boolean rings with a unit endowed with a link relation and as morphisms all compatible Boolean rings with unit morphisms. Furthermore, we study connectedness from an algebraic point of view, in the context of the proposed generalized Stone duality.

Abstract: The unitary irreducible representations of the unitary group U (n) are obtained from a more general set of polynomials that satisfy the multiplication rule for representations for arbitrary indeterminates. These polynomials are the familiar boson polynomials that appeared in earlier work, but are now presented from a new viewpoint. The main results are (1) the proof that these same polynomials provide a basis for all U (n) irreducible tensor operators when the commuting indeterminates are replaced by non-commuting fundamental unit tensor operators, and (2) the construction of all sets of unit tensor operators whose matrix elements give U (n) Clebsch-Gordan coefficients that possess the null space required by the Littlewood-Richardson numbers. Recent advances in the combinatorial interpretations of some of these results are pointed out. An outline is given of how the factorial Schur functions were discovered during the investigation of the properties of certain polynomials that characterize the null space of U (3) tensor operators.

Abstract: This paper is a study of cohomology and extensions of hypo- ˇ Silov modules over unit modulus algebras. We first prove that every C(@AU)- extension of a hypo-ˇ module, viewed as a Hilbert module over AU, is projective and injective. It follows that some interesting results are derived, especially so-called "Hom-Isomorphism" theorem. By using "Hom-Ext" se- quences, we can compute ExtAU-groups for hypo- ˇ Silov modules and cohypo- ˇ Silov modules. Finally, these results are applied to the discussion of rigidity and extensions of Hardy submodules over polydisk algebras.

Abstract: The attachment (12), especially foot-rest is adjustable by at least one electrically operated drive unit (14,16) and has at least one pressure-sensitive element (18). The drive unit and pressure-sensitive element are connected by a control unit (22). The pressure-sensitive element is connected to a contact element by which pressure exerted on the contact side of the contact element is transmitted to the pressure-sensitive element. At least one pressure-sensitive surface of the element is completely covered by the contact element.

Abstract: Discusses the merits of implementing a character education curriculum through teaching literature according to themes. Argues that a reflective approach, emphasizing students’ engagement with the issues and the resolutions they come up with for considering moral dilemmas, will be more effective than a didactic approach. Describes a unit on success, part of an American literature class for high school juniors.

Abstract: Centers of integral group rings are studied. The notion of a class character ring is introduced and made use of in describing centers of integral group rings. With every automorphism of a character field, associated is an automorphism of the center of an integral group ring. The norm of a central element of an integral group ring is determined and used to obtain invertibility criteria for central elements.

Abstract: Abstract An underlying theme of the contributions in this book is that firms find themselves embedded in internal and external networks of relationships within which there are neither ‘pure’ arm’s-length nor formal hierarchical transactions. It follows that it is these relationships-rather than the nodes per se that are of primary interest. It has also been posited that capabilities are nourished and grow in such networks. Essentially we are then left with ‘the firm’ defined as a legal entity and with a claim to be the natural and only unit of analysis. This is problematic as we then lack unambiguous terminology for identifying the ‘correct’ unit(s) of analysis. Many of the contributions point to capabilities residing at different organizational levels.

Abstract: One of our main results is a theorem on the existence of a left unit in Banach algebras. As a consequence, we obtain a non-commutative version of a result due to Dixon.

Abstract: Direct constructions of Diophantine representations for linear recurrent sequences are considered. Diophantine representations of the sets of values for third-order sequences with negative discriminants are found. As an auxiliary problem, we study the structure of the multiplicative group of the ringZ[λ], where λ is an invertible algebraic integer (unit) in a real quadratic field or in a cubic field of negative discriminant. The index of the subgroup {±λ n ∣n ∈Z} in the group (Z[λ])* and the generator of (Z[λ])* are evaluated explicitly. Bibliography: 14 titles.

Abstract: Consider the multiplicative semigroup M (S) of all probability distribution functions on subsets S of 2 . This structure corresponds to the coordinatewise maximum of S-valued independent random vectors. We provide a wide class of possible territories S, where in spite of the lack of the unit element in M (S), there is a Khinchine-type decomposition. In case M (S) has a unit element, we characterize the subsets S with the property that there is a decomposition in M (S).