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We introduce the cohomological blowup of a graded Artinian Gorenstein algebra along a surjective map, which we term BUG (blowup Gorenstein) for short. This is intended to translate to an algebraic context the cohomology ring of a blowup of a projective manifold along a projective submanifold. We show, among other things, that a BUG is a connected sum, that it is the general fiber in a flat family of algebras, and that it preserves the strong Lefschetz property. We also show that standard graded compressed algebras are rarely BUGs, and we classify those BUGs that are complete intersections. We have included many examples throughout this manuscript.

We show that the ideal generated by maximal minors (i.e., $(k+1)$-minors) of a $(k+1) \times n$ Vandermonde matrix is radical and Cohen-Macaulay. Note that this ideal is generated by all Specht polynomials with shape $(n-k,1,...,1)$., Comment: 6 pages, simplified the proof of the main result. To appear in Math. Scand

We show that the Specht ideal of a two-rowed partition is perfect over an arbitrary field, provided that the characteristic is either zero or bounded below by the size of the second row of the partition, and we show this lower bound is tight. We also establish perfection and other properties of certain variants of Specht ideals, and find a surprising connection to the weak Lefschetz property. Our results in particular give a self-contained proof of Cohen-Macaulayness of certain $h$-equals sets, a result previously obtained by Etingof-Gorsky-Losev over the complex numbers using rational Cherednik algebras., 42 pages, 2 figures

We give a detailed proof for Gordan-Noether’s results in “Ueber die algebraischen Formen, deren Hesse’sche Determinante identisch verschwindet.” C. Lossen has written a paper in a similar direction as the present paper, but did not provide a proof for every result. In our paper, every result is proved. Furthermore, our paper is independent of Lossen’s paper and includes a considerable number of new observations.

We relate the Weyr structure of a square matrix B to that of the t × t block upper triangular matrix C that has B down the main diagonal and first superdiagonal, and zeros elsewhere. Of special interest is the case t = 2 and where C is the nth Sierpinski matrix B n , which is defined inductively by B 0 = 1 and B n = [ B n − 1 B n − 1 0 B n − 1 ] . This yields an easy derivation of the Weyr structure of B n as the binomial coefficients arranged in decreasing order. Earlier proofs of the Jordan analogue of this had often relied on deep theorems from such areas as algebraic geometry. The result has interesting consequences for commutative, finite-dimensional algebras.

Let $\mathcal {V}=\bigsqcup _{i=0}^n\mathcal {V}_i$ be the lattice of subspaces of the $n$-dimensional vector space over the finite field $\mathbb{F} _q$, and let $\mathcal {A}$ be the graded Gorenstein algebra defined over $\mathbb{Q} $ which has $\mathcal {V}$ as a $\mathbb{Q} $ basis. Let $F$ be the Macaulay dual generator for $\mathcal {A}$. We explicitly compute the Hessian determinant $|{\partial ^2F}/{\partial X_i \partial X_j}|$, evaluated at the point $X_1 = X_2 = \cdots = X_N=1$, and relate it to the determinant of the incidence matrix between $\mathcal {V}_1$ and $\mathcal {V}_{n-1}$. Our exploration is motivated by the fact that both of these matrices naturally arise in the study of the Sperner property of the lattice and the Lefschetz property for the graded Artinian Gorenstein algebra associated to it.

We prove the strong Lefschetz property for certain complete intersections defined by products of linear forms, using a characterization of the strong Lefschetz property in terms of central simple modules., Comment: 9 pages

Let $F$ be a homogeneous polynomial in $n$ variables of degree $d$ over a field $K$. Let $A(F)$ be the associated Artinian graded $K$-algebra. If $B \subset A(F)$ is a subalgebra of $A(F)$ which is Gorenstein with the same socle degree as $A(F)$, we describe the Macaulay dual generator for $B$ in terms of $F$. Furthermore when $n=d$, we give necessary and sufficient conditions on the polynomial $F$ for $A(F)$ to be a complete intersection.

Risperidone (RIS) is a frequently used efficacious psychotropic drug. However, it prolongs the QTc interval and may cause fatal arrhythmia. Little is known on the determinants of this RIS side effect. RIS is metabolized by CYP2D6, and is subject to drug efflux by P-glycoprotein (P-gp) encoded by the ATP-binding cassette subfamily B member 1 (ABCB1) gene. P-gp removes both RIS and its metabolite 9-OH-RIS from cardiac tissue. To investigate the effect of RIS metabolism and ABCB1 gene polymorphisms on QTc, steady-state plasma RIS and 9-OH-RIS levels, and QTc were measured. CYP2D6, ABCB1 C3435T and G2677T/A genotypes were determined in 66 schizophrenia patients on RIS. QTc was significantly longer in patients with ABCB1 3435CT+3435 TT than in those with 3435CC (P=0.006). ABCB1 G2677T/A genotype did not affect QTc. Multiple regression analysis showed that C/T or T/T genotypes at the ABCB1 C3435T locus, lower weight, and older age prolonged QTc. In summary, the T allele of the ABCB1 C3435T genotype should be considered in future diagnostic development efforts for RIS-associated QT.

A homogeneous ideal $I$ of a polynomial ring $S$ is said to have the Rees property if, for any homogeneous ideal $J \subset S $ which contains $I$, the number of generators of $J$ is smaller than or equal to that of $I$. A homogeneous ideal $I \subset S$ is said to be $\mathfrak m$-full if $\mathfrak mI:y=I$ for some $y \in \mathfrak m$, where $\mathfrak m$ is the graded maximal ideal of $S$. It was proved by one of the authors that $\mathfrak m$-full ideals have the Rees property and that the converse holds in a polynomial ring with two variables. In this note, we give examples of ideals which have the Rees property but are not $\mathfrak m$-full in a polynomial ring with more than two variables. To prove this result, we also show that every Artinian monomial almost complete intersection in three variables has the Sperner property., Comment: 8 pages

Aims In Europe and North America, schizophrenia patients treated with antipsychotic agents have a higher prevalence of obesity and metabolic syndrome compared with healthy individuals. In Japan, the prevalence of overweight/obesity in the general population is considerably lower than that in Europe and North America. The purpose of this study was to investigate the prevalence of underweight and overweight/obesity as well as laboratory data in Japanese inpatients with schizophrenia. Methods The subjects were 333 inpatients with schizophrenia and 191 age- and sex-matched healthy volunteers. Overweight/obesity was defined as body mass index (BMI) ≥ 25 kg/m2, standard weight was defined as BMI ≥ 18.5 to

We compute the resultants for quadratic binomial complete intersections. As an application we show that any quadratic binomial complete intersection can have the set of square-free monomials as a vector space basis if the generators are put in a normal form., Comment: 14 pages

Let $A$ be a graded complete intersection over a field and $B$ the monomial complete intersection with the generators of the same degrees as $A$. The EGH conjecture says that if $I$ is a graded ideal in $A$, then there should be an ideal $J$ in $B$ such that $B/J$ and $A/I$ have the same Hilbert function. We show that if the EGH conjecture is true, then it can be used to prove that every graded complete intersection over any field has the Sperner property., Comment: 7 pages

2 Preliminaries 5 2.1 A list of notational conventions . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The equi-degree monomial complete intersection as a tensor space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Young tableaux and Specht polynomials . . . . . . . . . . . . . . . . . . . . 6 2.4 Nilpotent matrices and Jordan bases . . . . . . . . . . . . . . . . . . . . . . 6 2.5 The strong Lefschetz property . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Let B be the Boolean lattice on an n-set with B=@?B"i the rank decomposition. Let M(n,i) be the incidence matrix between B"i and B"n"-"i. We obtain a recursive formula for the determinant of the matrix M(n,i).

We prove that any quadratic complete intersection with a certain action of the symmetric group has the strong Lefschetz property over a field of characteristic zero. Furthermore, we discuss under what conditions its ring of invariants by a Young subgroup is a homogeneous complete intersection with a standard grading.

弁膜症手術においては,系統的な術中希釈式自己血輸血(以下,D法)の報告はこれまでになく,近年は手術症例の病態の重篤化などに伴い術前貯血も必ずしも施行できない.そこで,その評価を本研究で試みた.1998～2004年の術前自己血貯血未施行の成人弁膜症手術症例中,大動脈置換術などを伴う症例を除外し,D法を施行した25例を対象とした.同種血無輸血群は18例,同種血輸血群は7例であった.体外循環離脱後に各群2例に回収式自己血輸血を施行した.両群において,男女比,術式,体重,体外循環による希釈率,体外循環時間およびヘマトクリットの推移などに差を認めなかった.しかし,D法に伴う体重当たりの術中貯血量は同種血輸血群が有意に少なかった(11.3±2.5 vs 7.3±1.8ml/kg,p

A 53-year-old Japanese man with fulminant myocarditis was referred. Percutaneous cardiopulmonary support (PCPS) was introduced immediately and intravenous immunoglobulin (IVIG) therapy followed for 2 days. Cardiac function showed signs of recovery on the 4th hospital day and the patient was weaned from PCPS on the 7th hospital day. Creatine kinase-MB peaked at 12 h after admission and was 176 ng/ml. Endomyocardial biopsy showed active myocarditis. A marked increase of the neutralizing antibody titer suggested coxsackievirus B3 infection. Plasma concentrations of cytokines and neurohumoral factors were analyzed. Proinflammatory cytokines, such as interleukin (IL)-1beta, IL-6 and tumor necrosis factor (TNF-alpha), and anti-inflammatory cytokines, such as IL-1 receptor antagonist, soluble TNF receptor-1 and IL-10, were elevated on admission and all had decreased on the 7th hospital day. Brain natriuretic peptide and noradrenaline were already elevated upon admission (1,940 pg/ml and 4.6 ng/ml, respectively) and decreased thereafter. Although IVIG therapy under PCPS is a common treatment for fulminant myocarditis, the immunological response in vivo remains unclear. This case demonstrated suppression of serum cytokines after IVIG and PCPS treatment. Immunological parameters in those who have been treated with IVIG and PCPS and survived without complications are of great value for evaluation of the therapy. Further analysis with more cases in a multicenter study is necessary.

Let A = bigoplus_{i >= 0} A_i be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element ell of degree 1 such that the multiplication times ell : A_i --> A_{i+1} has maximal rank, for every i, and A has the Strong Lefschetz property if times ell^d : A_i --> A_{i+d} has maximal rank for every i and d. The main results obtained in this paper are the following. 1) EVERY height three complete intersection has the Weak Lefschetz property. (Our method, surprisingly, uses rank two vector bundles on P^2 and the Grauert-Mulich theorem.) 2) We give a complete characterization (including a concrete construction) of the Hilbert functions that can occur for K-algebras with the Weak or Strong Lefschetz property (and the characterization is the same one). 3) We give a sharp bound on the graded Betti numbers (achieved by our construction) of Artinian K-algebras with the Weak or Strong Lefschetz property and fixed Hilbert function. This bound is again the same for both properties. Some Hilbert functions in fact FORCE the algebra to have the maximal Betti numbers. 4) EVERY Artinian ideal in K[x,y] possesses the Strong Lefschetz property. This is false in higher codimension., To appear in J. Algebra

We show that the class of completely m-full ideals coincides with the class of componentwise linear ideals in a polynomial ring over an infinite field., 12 pages

Exploring functional polymorphisms in the dopamine receptor D2 gene using prolactin concentration in healthy subjects

Let k k be a field of characteristic 0. If I ⊂ k [ x , y , z ] I \subset k[x,y,z] is a complete intersection generated by three homogeneous elements of degrees d 1 , d 2 , d 3 d_1,d_2,d_3 with 2 ≤ d 1 ≤ d 2 ≤ d 3 2 \le d_1 \le d_2 \le d_3 , then the reduction of I I by a general linear form is minimally generated by three elements if and only if d 3 ≤ d 1 + d 2 − 2 d_3 \le d_1+d_2-2 .

We examined the difference between the effects of olanzapine (OLZ) and risperidone (RIS) on PR and QT intervals among patients with stable schizophrenia using a cohort analysis.Twenty-one subjects treated with OLZ were enrolled in the study. Following baseline assessments, which included PR and QT intervals, OLZ was switched to RIS for each subject. The same parameters were evaluated following the switch to RIS.All patients who had been treated with OLZ were successfully switched to RIS. In all patients, we observed a significant decrease in PR interval (t = 2.397, P = 0.029) and no change in either QTc or RR interval. In female patients, the QTc interval was significantly decreased (t = 3.495, P = 0.008) following the switch, while in male patients, the QTc interval did not change. No patients showed a PR interval of200 ms or a QTc interval of500 ms.OLZ treatment has a greater prolonging effect on PR and QT intervals compared with RIS. Careful attention may need to be paid to the cardiac conduction system in addition to QT prolongation during OLZ treatment.

Background Olanzapine (OLZ) treatment is associated with a high risk of weight gain, and may cause abnormalities in glycolipid metabolism. Therefore, the underlying mechanism of OLZ-related weight gain is needed to clarify but not yet been adequately determined. In recent years, adipocytokines such as leptin, adiponectin, and tumor necrosis factor (TNF)-α, which play important roles in energy homeostasis, have been suggested as biomarkers of weight gain. Here, we determined if baseline plasma concentrations of leptin, adiponectin, and TNF-α predict weight gain following OLZ treatment. Methods We recruited 31 schizophrenia outpatients (12 men and 19 women, 28.8 ± 10.2 years old) that were unmedicated or on another antipsychotic monotherapy medication. Baseline body mass index (BMI) and plasma levels of leptin, adiponectin, and TNF-α were obtained. All patients started or were switched to OLZ monotherapy for a maximum of 1 year. BMI was also obtained at the endpoint. Results Mean BMI change following OLZ treatment was 2.1 ± 2.7 kg/m2. BMI change from baseline to endpoint negatively-correlated with baseline leptin levels in female patients (r = −0.514, P = 0.024), but not male patients. Baseline adiponectin or TNF-α levels were not correlated with BMI change. Conclusion Baseline plasma leptin can have an effect on subsequent weight gain following OLZ treatment in female patients with schizophrenia.

In Europe and North America, schizophrenia patients treated with antipsychotic agents have a higher prevalence of obesity and metabolic syndrome compared with healthy individuals. In Japan, the prevalence of overweight/obesity in the general population is considerably lower than that in Europe and North America. The purpose of this study was to investigate the prevalence of underweight and overweight/obesity as well as laboratory data in Japanese inpatients with schizophrenia.The subjects were 333 inpatients with schizophrenia and 191 age- and sex-matched healthy volunteers. Overweight/obesity was defined as body mass index (BMI) ≥ 25 kg/m(2) , standard weight was defined as BMI ≥ 18.5 to25 kg/m(2) and underweight was defined as BMI 18.5 kg/m(2) .A significant difference in the prevalence of the three BMI levels was observed between schizophrenia patients and controls (P 0.001). The prevalence of underweight was significantly higher in schizophrenia patients than that in controls (P 0.001). The prevalence of hypoproteinemia (P 0.001) and of hypocholesterolemia (P 0.001) were significantly higher in schizophrenia patients than in controls. In schizophrenia patients, the prevalence of hypotriglyceridemia was significantly higher in the underweight group than in the standard weight group (P = 0.003) and in the overweight/obesity group (P 0.001).The prevalence of underweight in Japanese inpatients with schizophrenia may be higher compared with that in the general population. Therefore, the physical health of inpatients should be more carefully taken into account in clinical practice.

We show a number of properties of the commutator algebra of a nilpotent matrix over a field. In particular we determine the simple modules of the commutator algebra. Then the results are applied to prove that certain Artinian complete intersections have the strong Lefschetz property.

We give a necessary and sufficient condition for a standard graded Artinian ring of the form $K[x_{1},\ldots,x_{n}]/I$, where $I$ is an ${\mathfrak{m}}$-full ideal, to have the weak Lefschetz property in terms of graded Betti numbers. This is a generalization of a theorem of Wiebe for componentwise linear ideals. We also prove that the class of componentwise linear ideals and that of completely ${\mathfrak{m}}$-full ideals coincide in characteristic zero and in positive characteristic, with the assumption that $\mathrm{Gin}(I)$ w.r.t. the graded reverse lexicographic order is stable.

Several studies have shown increased rates of hyperglycemia and diabetes in schizophrenic patients treated with olanzapine. However, the underlying mechanism is poorly understood. Glucose-dependent insulinotropic polypeptide (GIP) is known to affect insulin secretion by pancreatic β cells. Recently, a meta-analysis study reported an association between a GIP receptor (GIPR) gene polymorphism (rs10423928) and insulin secretion measured by an oral glucose tolerance test (OGTT). We assessed the influence of this GIPR gene polymorphism on glucose metabolism in 60 schizophrenic patients treated with olanzapine and 103 healthy controls. The GIPR gene polymorphism was determined using TaqMan methods. We performed repeated-measures analysis of variance (ANOVA) and one-way ANOVA for the glucose and insulin levels during OGTTs in four groups divided by the GIPR gene polymorphism and cohort (schizophrenia or control). We found significant effects of the GIPR gene and cohort on the insulin levels at 30 min. Our findings suggest that schizophrenic patients with the A allele of GIPR rs10423928 are at risk of developing hyperinsulinemia when treated with antipsychotics.

We give a characterization of the Lefschetz elements in Artinian Gorenstein rings over a field of characteristic zero in terms of the higher Hessians. As an application, we give new examples of Artinian Gorenstein rings which do not have the strong Lefschetz property.

We define the strong Lefschetz property for finite graded modules over graded Artinian algebras whose grading is not necessarily standard. We show that most results which have been obtained for Artinian algebras with standard grading can be extended for non-standard grading. Our results on the strong Lefschetz property for non-standard grading can be used to prove that certain Artinian complete intersections with standard grading have the strong Lefschetz property., 24 pages, To appear in Journal of Algebra

Let A be a standard graded Artinian algebra over a field of characteristic zero and let z be a linear form in A. We define the central simple modules for each such pair (A, z). Assume that A is Gorenstein. Then we prove that A has the strong Lefschetz property if and only if there exists a linear form z in A such that all central simple modules of the pair (A,z) have the strong Lefschetz property. In the course of proof we need to extend the definition of the strong Lefschetz property to finite graded modules over graded Artinian algebra, which previously was defined only for standard graded Artinian algebras., Comment: 20 pages, To be published in Journal of Pure and Applied Algebra

The notations used in this paper without explicit mention are listed below. Here R is a positively graded Noetherian ring, a a homogeneous ideal of R, and f, g, …, h are homogeneous elements of R.

An ideal a of a local ring (R, m) is called m-full if am: y = a for some y in a certain faithfully flat extension of R. The definition is due to Rees (unpublished) and he had obtained some elementary results (also unpublished). The present paper concerns some basic properties of m-full ideals. One result is the characterization of m-fullness in terms of the minimal number of generators of ideal, generalizing his result in a low dimensional case (Theorem 2, § 2).

Let A = R/, where R is a regular local ring of arbitrary dimension and is an ideal of R. If A is a Gorenstein ring and if height = 2, it is easily proved that A is a complete intersection, i.e., is generated by two elements (Serre [5], Proposition 3). Hence Gorenstein rings which are not complete intersections are of embedding codimension at least three. An example of these rings is found in Bass’ paper [1] (p. 29). This is obtained as a quotient of a three dimensional regular local ring by an ideal which is generated by five elements, i.e., generated by a regular sequence plus two more elements. In this paper, suggested by this example, we prove that if A is a Gorenstein ring and if height = 3, then is minimally generated by an odd number of elements. If A has a greater codimension, presumably there is no such restriction on the minimal number of generators for , as will be conceived from the proof.

1Let A be an Artin local ring. The Dilworth number of A is defined to be the supremum of p(Z) for ideals Z in A, where p is the minimal number of generators. In my paper [4], I developed some methods to compute this number when A is homogeneously graded over a field k, and especially if A is Gorenstein and ch k = 0, I showed that it is the dominating case that the Dilworth number is attained by a power of the maximal ideal. In such a case we shall say that A has the Sperner property. In the present paper we consider Artin rings (A, m), not necessarily graded, and compare the Dilworth number of A and that of Gr,(A), and it will be shown that the main result of [4] is valid without the assumption that the rings are homogeneous. Our main result is Theorem 7, where we prove that “most” Artin Gorenstein rings have the Sperner property. (Actually we prove a stronger result, which says that it has the “weak Stanley property.“) To explain the term “most,” we represent an Artin Gorenstein ring A in the

Denote by p_k the k-th power sum symmetric polynomial n variables. The interpretation of the q-analogue of the binomial coefficient as Hilbert function leads us to discover that n consecutive power sums in n variables form a regular sequence. We consider then the following problem: describe the subsets n powersums forming a regular sequence. A necessary condition is that n! divides the product of the degrees of the elements. To find an easily verifiable sufficient condition turns out to be surprisingly difficult already in 3 variables. Given positive integers a, Comment: corrected a typo in Lemma 2.4(b)