Bone loss with aging results from attenuated and unbalanced bone turnover that has been associated with a decreased number of bone forming osteoblasts, an increased number of bone resorbing osteoclasts, and an increased number of adipocytes (fat cells) in the bone marrow. Osteoblasts and adipocytes are derived from marrow mesenchymal stroma/stem cells (MSC). The milieu of intracellular and extracellular signals that controls MSC lineage allocation is diverse. The adipocyte-specific transcription factor peroxisome proliferator-activated receptor-gamma (PPAR-γ) acts as a critical positive regulator of marrow adipocyte formation and as a negative regulator of osteoblast development.In vivo, increased PPAR-γactivity leads to bone loss, similar to the bone loss observed with aging, whereas decreased PPAR-γactivity results in increased bone mass. Emerging evidence suggests that the pro-adipocytic and the anti-osteoblastic properties of PPAR-γare ligand-selective, suggesting the existence of multiple mechanisms by which PPAR-γcontrols bone mass and fat mass in bone.
In the course of an investigation of the β-ray spectrum of Ra (B + C) by the ionisation method, Chadwick(1) concluded that the line spectrum is superimposed on a strong continuous background. The ionisation method, however, is not one which admits of high resolving power, and doubts have been entertained whether the continuous spectrum has in fact any real existence. In this connection the case of Ra E is one of special importance, since no line spectrum from this body has been detected by the more sensitive photographic method. Experiments have therefore been undertaken with the object of determining the distribution with velocity of the numbers of particles in the β-ray spectrum of Ra E.
The relative amounts of Ra‐224, Ra‐226, and Ra‐228 in a number of petroleum brine samples from Oklahoma and northwestern Arkansas have been determined. The highest concentration found was more than one millimicrocurie/liter of brine. Some brines contained radium isotopes characteristic of the thorium series, others contained Ra‐226 which is characteristic of the uranium series, while others contained radium from both the thorium and uranium series. The radium isotopes in the brines are not in radioactive equilibrium with their uranium and thorium parents.
In 1967 Foulser [1] defined a class of translation planes, called generalized André planes or λ-planes and discussed the associated autotopism collineation groups. While discussing these collineation groups he raised the following question:“Are there collineations of a λ plane which move the axes but do not interchange them?”.In this context, Foulser mentioned a conjecture of D. R. Hughes that among the André planes, only the Hall planes have collineations moving the axes without interchanging them. Wilke [4] answered Foulser's question partially by showing that the conjecture of Hughes is indeed correct. Recently, Foulser [2] has shown that possibly with a certain exception the Hall planes are the only generalized André planes which have collineations moving the axes without interchanging them. Our aim in this paper is to give an alternate proof, which is completely general, and is in the style of the original problem.
The purpose of this paper is to prove the following theorem of uniform Artin-Rees properties: Let $A$ be an excellent (in fact J-2) ring and let $N\subset M$ be two finitely generated $A$-modules such that ${\rm dim}(M/N)\leq 1$. Then there exists an integer $s\geq 1$ such that, for all integers $n\geq s$ and for all ideals $I$ of $A$, $I^{n}M\cap N=I^{n-s}(I^{s}M\cap N)$.
We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive characteristic in terms of Hasse-Schmidt derivations
Criteria are given in terms of certain Hilbert coefficients for the fiber cone F(I) of an m-primary ideal I in a Cohen-Macaulay local ring (R,m) so that it is Cohen-Macaulay or has depth at least dim(R)-1. A version of Huneke's fundamental lemma is proved for fiber cones. S. Goto's results concerning Cohen-Macaulay fiber cones of ideals with minimal multiplicity are obtained as consequences.
Let $Q=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ with the standard $N^n$-grading. Let $φ$ be a morphism of finite free $N^n$-graded $Q$-modules. We translate to this setting several notions and constructions that appear originally in the context of monomial ideals. First, using a modification of the Buchsbaum-Rim complex, we construct a canonical complex $T_\bullet(φ)$ of finite free $N^n$-graded $Q$-modules that generalizes Taylor's resolution. This complex provides a free resolution for the cokernel $M$ of $φ$ when $φ$ satisfies certain rank criteria. We also introduce the Scarf complex of $φ$, and a notion of ``generic'' morphism. Our main result is that the Scarf complex of $φ$ is a minimal free resolution of $M$ when $φ$ is minimal and generic. Finally, we introduce the LCM-lattice for $φ$ and establish its significance in determining the minimal resolution of $M$.
Let $(R,\fm,k)$ be a commutative noetherian local ring with dualizing complex $\dua R$, normalized by $\Ext^{\depth(R)}_R(k,\dua R)\cong k$. Partly motivated by a long standing conjecture of Tachikawa on (not necessarily commutative) $k$-algebras of finite rank, we conjecture that if $\Ext^n_R(\dua R,R)=0$ for all $n>0$, then $R$ is Gorenstein, and prove this in several significant cases.
Let R = k[[x_0,...,x_d]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x_0,...,x_d]]. We investigate the question of which rings of this form have bounded Cohen--Macaulay type, that is, have a bound on the multiplicities of the indecomposable maximal Cohen--Macaulay modules. As with finite Cohen--Macaulay type, if the characteristic is different from two, the question reduces to the one-dimensional case: The ring R has bounded Cohen--Macaulay type if and only if R is isomorphic to k[[x_0,...,x_d]]/(g+x_2^2+...+x_d^2), where g is an element of k[[x_0,x_1]] and k[[x_0,x_1]]/(g) has bounded Cohen--Macaulay type. We determine which rings of the form k[[x_0,x_1]]/(g) have bounded Cohen--Macaulay type.
We give conjectures on the "asymptotic" behaviour of the Hilbert series of (quotients by) generic ideals in the exterior algebra, as the number of variables tend to infinity. Our conjectures are supported by extensive computer calculations.
We prove asymptotic linear bounds for the Castelnuovo-Mumford regularity of certain filtrations of homogeneous ideals whose Rees algebras need not to be Noetherian.
In this paper we study homological properties of the Rees ring R of the graded maximal ideal of a standard graded k-algebra A. In particular we are interested the comparison of the depth and regularity of A and R.
We give three determinantal expressions for the Hilbert series as well as the Hilbert function of a Pfaffian ring, and a closed form product formula for its multiplicity. An appendix outlining some basic facts about degeneracy loci and applications to multiplicity formulae for Pfaffian rings is also included.
Let X be a set of smooth points in P^2, and I = \oplus_{t >= d} I_t the defining ideal of X. In this paper, we give a set of defining equations for the Rees algebra R(I_{d+1}) of the ideal generated by I_{d+1}. This study give information to completely answer questions on the defining ideals of projective embeddings of the blowup of P^2 along the points in X, which has been studied by many authors. In this paper, we also study the asymptotic behaviour of the Rees algebras R(I_t) of the ideal generated by I_t, as t gets large.
The principal result is a primary decomposition of ideals generated by the (2x2)-subpermanents of a generic matrix. These permanental ideals almost always have embedded components and their minimal primes are of three distinct heights. Thus the permanental ideals are almost never Cohen-Macaulay, in contrast with determinantal ideals.
We associate to each $r$-multigraded, locally finitely generated ideal in the "large polynomial ring" on countably many indeterminates a power series in $r$ variables; this power series is the limit in the adic topology of the numerators of the rational functions which give the Hilbert series of the truncations of the ideal. We characterise the set of all power series so obtained. Our main technical tools are an approximation result which asserts that truncation and the forming of initial ideals commute in a filtered sense, and standard inclusion/exclusion, Möbius inversion, and LCM-lattice homology methods generalised to monomial ideals in countably many variables.