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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

BACKGROUND Users of antipsychotics (APs) have a risk of sudden cardiac death (SCD). Sudden cardiac death in such patients is thought to be largely due to drug-induced QT prolongation. It has been reported that many subjects with drug-induced torsades de pointes (TdP) have risk alleles associated with subclinical congenital long QT syndrome. METHODS We investigated the effects of the risk alleles associated with long QT on the QT interval in patients receiving APs using 24-hour Holter electrocardiograms to take into account the circadian fluctuation of QT intervals. We investigated 8 single-nucleotide polymorphisms identified on a GWAS. RESULTS We found that increased numbers of risk alleles at rs7188697 in NDRG4 and rs11970286 in PLN were the major predictors of an increased maximum QT interval over 24 hours in users of APs. CONCLUSIONS It could be useful to perform a DNA-based analysis before the initiation of APs to reduce the risk of drug-induced torsades de pointes and SCD.

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.

Association between gastric inhibitory polypeptide receptor polymorphism, rs10423928, and body mass index in olanzapine-treated schizophrenia was examined. Body mass index change for the A/T+A/A genotypes was significantly higher than that for the T/T genotype. rs10423928 may predict weight gain in schizophrenia.

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

9-Hydroxyrisperidone (9-OH-RIS) is an active metabolite of the antipsychotic drug risperidone (RIS). The total active moiety level, in other words the sum of the RIS and 9-OH-RIS serum levels, may be important for estimating the clinical effects of RIS treatment. However, there have been no consistent results reported regarding the relationship between cytochrome P450 (CYP) 2D6 or adenosine triphosphate-binding cassette subfamily B member 1 (ABCB1) variant alleles and 9-OH-RIS or total active moiety plasma levels. Seventy-four Japanese patients treated with RIS were examined in the present study. Steady-state plasma RIS and 9-OH-RIS were measured. The CYP2D6*5, CYP2D6*10, ABCB1 3435C>T, and ABCB1 2677G>T/A genotypes were detected. Multiple regression analysis showed that the dose-corrected plasma RIS levels were significantly correlated with the number of CYP2D6 variant alleles and ABCB1 3435C>T genotypes, whereas the 9-OH-RIS and total active moiety levels were significantly correlated with the ABCB1 3435C>T genotypes and with age. On the other hand, the ABCB1 2677G>T/A genotypes did not affect plasma RIS, 9-OH-RIS, or total active moiety levels. The ABCB1 3435C>T genetic polymorphism may predict plasma 9-OH-RIS and total active moiety levels.

Objective We examined sex differences in the effect of olanzapine (OLZ), risperidone (RIS), aripiprazole (ARP), or quetiapine (QTP) on mean corrected QT (QTc) intervals among 222 patients with schizophrenia. Methods Subjects were patients with schizophrenia who were treated with either OLZ (n = 69), RIS (n = 60), ARP (n = 62), or QTP (n = 31). Electrocardiographic measurements were conducted, and the QT interval was corrected using Bazett's correction formula. Results The mean QTc interval of the QTP group was significantly longer than that of the RIS group (p = 0.002) or ARP group (p = 0.029). The mean QTc interval of the OLZ group was also significantly longer than that of the RIS group (p = 0.006). In female participants, the difference in the mean QTc interval among the four second-generation antipsychotic (SGA) groups was statistically significant (p = 0.002), whereas in male patients, there was no significant difference in the mean QTc interval among the four SGA groups. Post hoc analyses showed that sex differences in QTc interval were observed only in OLZ treatment group (p = 0.007). Conclusion To our knowledge, this is the first study to demonstrate sex differences in the effect of four SGAs on the QTc interval. Copyright © 2013 John Wiley & Sons, Ltd.

Although second-generation antipsychotics (SGAs) are characterized by fewer prolactin (PRL)-related side effects compared with first-generation antipsychotics, the detailed effects of SGAs on the plasma PRL levels still remain unclear. We examined the differences in plasma PRL levels among 268 patients treated for schizophrenia with olanzapine (OLZ), risperidone (RIS), aripiprazole (ARP), quetiapine (QTP), or perospirone (PER). The participants had received antipsychotic monotherapy with stable doses of OLZ, RIS, ARP, QTP, or PER for ≥ 3 weeks, and fasting blood samples were drawn to examine plasma PRL levels. The differences in median plasma PRL levels in all (P

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

The underlying mechanism for second-generation antipsychotic (SGA)-related glucose-lipid metabolic dysfunction is not fully understood. Recent studies have suggested a possible impact of SGAs on endocrine regulation, especially on adipocytokines. We examined the effect of each SGA on various adipocytokines in normal fasting glucose (NFG) subjects.The study population comprised 113 Japanese inpatients with schizophrenia who were treated with olanzapine, risperidone, or quetiapine, and 123 healthy control (CONT) volunteers. All of the subjects were diagnosed with NFG. Plasma concentration of adiponectin, leptin, tumor necrosis factor α, total cholesterol, triglyceride, high-density lipoprotein cholesterol, and low-density lipoprotein cholesterol were compared between the SGA and CONT groups.Second-generation antipsychotic subjects had significantly higher leptin levels in comparison to the CONT subjects. The plasma concentration of adiponectin, total cholesterol, and high-density lipoprotein cholesterol in the SGA subjects were significantly lower than those in the CONT subjects. There were no significant differences in tumor necrosis factor α, triglyceride, and low-density lipoprotein cholesterol levels between the 2 groups. In a stepwise multiple regression analysis, olanzapine was found to be a factor that contributed to decreased adiponectin levels, and the CONT subjects were detected to be a factor associated with lower leptin levels.The present study indicates the possibility that the administration of SGAs may affect adipocytokines in the NFG stage, excluding the impaired fasting glucose group, which is in the transition stage into diabetes mellitus.

Most antipsychotic agents can cause QT prolongation, which causes torsades de pointes. The QT interval in healthy subjects is longer during nighttime than during daytime. The QT interval of patients treated with antipsychotics may be prolonged during nighttime, and the effects of antipsychotics on the QT interval may differ between antipsychotics. This study investigated the circadian dynamics of the QT interval in patients treated with antipsychotics and healthy controls, using a 24-hour Holter electrocardiogram in a clinical setting. Sixty-six patients with a diagnosis of schizophrenia that were treated with risperidone or olanzapine and 40 healthy volunteers were enrolled. The QT intervals were corrected using the Fridericia formula (QTcF = QT / RR). Mean ± SD nighttime QTcFs were 411.6 ± 29.0, 395.9 ± 21.2, and 387.8 ± 19.0 milliseconds (ms) in the risperidone, olanzapine, and control groups, respectively. The mean daytime QTcFs were 397.7 ± 23.4, 392.4 ± 18.9, and 382.6 ± 17.3 ms, respectively. The mean nighttime QTcF of the risperidone group was significantly longer than that of the olanzapine and control groups, although there was no significant difference in the mean daytime QTcF between the risperidone and olanzapine groups. The current study used 24-hour Holter electrocardiograms to reveal significantly longer QT intervals in the risperidone group especially during nighttime. In clinical practices, evaluations of the QT interval have been conducted over short periods in the daytime, but it is believed that such methods may not be able to fully elucidate the effects of antipsychotics on the QT interval.

Objective The sum of the serum levels of risperidone (RIS) and 9-hydroxyrisperidone (9-OH-RIS), which is the active moiety serum level, could be important for estimating the clinical effects of RIS. However, there have been no consistent results reported about the relationship between cytochrome P450 (CYP) 2D6*10 allele and plasma 9-OH-RIS or active moiety levels. We investigated the effect of the number of CYP2D6*10 alleles on steady-state plasma RIS, 9-OH-RIS, and active moiety levels in Japanese patients. Methods Steady-state plasma RIS, 9-OH-RIS, and active moiety levels were measured in 64 patients treated with an average dosage of 4.6 mg/day. Results The number of CYP2D6*10 alleles significantly affected dose-corrected plasma RIS levels (p = 0.001), and the median concentrations in ng/ml/mg were 0.94 (0 allele) vs. 1.73 (1 allele) vs. 3.05 (2 alleles). The number of CYP2D6*10 alleles did not affect plasma 9-OH-RIS or active moiety levels. Conclusion The present study shows that the number of CYP2D6*10 alleles affected plasma RIS levels but not plasma 9-OH-RIS and plasma active moiety levels. Because the plasma active moiety levels can influence antipsychotic effects or side effects, the genetic screening of the CYP2D6*10 allele for RIS in Asian populations may not be clinically important. Copyright © 2012 John Wiley & Sons, Ltd.

Objective A dose-dependent increase in risk of sudden cardiac death for the antipsychotic drug risperidone was reported. However, few reports have so far addressed QT prolongation associated with the use of risperidone or its major active metabolite, which is also used as a separate antipsychotic drug, paliperidone. Methods The present study evaluated associations between risperidone metabolism and QT interval in 61 psychiatric patients who had been receiving risperidone for ≥4 weeks at an average dosage of 4.7 mg/day. Plasma risperidone and paliperidone levels were measured and electrocardiographic measurements were also obtained. Results There was no correlation between risperidone dosage and QTc or plasma risperidone levels and QTc. However, there was a significant positive correlation between plasma paliperidone levels and QTc (r = 0.361; p = 0.004). There was no correlation between age and dose-corrected plasma risperidone levels or between age and QTc. There was a significant positive correlation between age and dose-corrected plasma paliperidone levels (r = 0.290; p = 0.023). Conclusion Clinically, paliperidone is considered to play a more important role in QT prolongation than risperidone. Copyright © 2011 John Wiley & Sons, Ltd.

We investigated the association between remission of depressive symptoms in fluvoxamine treatment and catechol- O -methyltransferase (COMT) gene. Sixteen SNPs in the COMT gene were investigated in 123 outpatients with major depression. Three single nucleotide polymorphisms located in the 5′ region were associated with remission in fluvoxamine-treated outpatients with moderate to severe depression.

The CYP2D6 enzyme is a capacity-limited high-affinity drug elimination pathway that metabolizes numerous psychiatric medicines. The capacity-limited nature of this enzyme suggests that drug dose may serve as an important factor that influence genotype–phenotype associations. However, dose dependency of CYP2D6 genotype contributions to drug elimination, and its interaction with environmental factors (e.g., smoking) did not receive adequate attention in translational study designs. Fluvoxamine is a selective serotonin reuptake inhibitor antidepressant. Fluvoxamine concentration is one of the factors previously linked to clinical remission in moderate to severe depression. We investigated the joint effect of smoking (an inducer of CYP1A2) and CYP2D6 genotype on interindividual variability in fluvoxamine steady-state concentration. Fluvoxamine concentration was measured in 87 patients treated with 50, 100, 150 or 200 mg/d. While CYP2D6 genotype significantly influenced fluvoxamine concentration in all four dose groups ( p 2) by CYP2D6 decreased as the dose of fluvoxamine increased. Smoking status (nonsmokers vs. smoking 20 or more cigarettes/d) significantly affected fluvoxamine concentration in the 50 mg/d group only ( p = 0.005). Together, CYP2D6 genotype and smoking status explained 23% of the variance in fluvoxamine concentration but only at the low 50 mg/d dose group. These findings contribute to evidence-based and personalized choice of fluvoxamine dose using smoking status and CYP2D6 genetic variation. Additionally, these data lend evidence for drug dose as an important variable in translational pharmacogenetic study design and pharmaceutical phenotype associations with capacity-limited drug metabolism pathways such as CYP2D6.

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).

Several studies have reported that the cytochrome P450 (CYP) 2D6 plays an important role in the fluvoxamine metabolism. However, some other studies have reported that the CYP2D6 genotype has no major impact on the fluvoxamine concentration. This study investigated the dose-dependent effect of CYP2D6-variant alleles on the steady-state fluvoxamine concentration. There were 23 patients whose plasma concentrations of fluvoxamine were measured at 4 doses (50, 100, 150, and 200 mg/d). The differences in the plasma fluvoxamine concentration were analyzed between 2 genotype groups divided by the number of CYP2D6-variant alleles (with 0 and 1 or 2 variant alleles). The results demonstrated the nonlinear kinetics of fluvoxamine metabolism, and the degree of nonlinear kinetics decreased as the dose was increased. Significant differences in fluvoxamine concentration were observed between the subjects with 0 variant alleles and the subjects with 1 or 2 variant alleles (P = 0.044) when they were treated by 50 mg of fluvoxamine. There were no significant differences in the plasma concentration of fluvoxamine at 100, 150, and 200 mg/d. The present study suggests that the effect of the CYP2D6 genotype on fluvoxamine metabolism is greater at lower doses of fluvoxamine.

UNLABELLED This study investigated effects of the 3435 C>T genotype of the adenosine triphosphate-binding cassette subfamily B member 1 (ABCB1, MDR1) gene on the steady-state plasma concentration of fluvoxamine (FLV). METHODS Sixty-two psychiatric patients were treated with different doses (50, 100, 150, and 200 mg/d) of FLV. Blood samples were collected after at least 2 weeks of treatment with the same daily dose to obtain steady-state concentrations of FLV, and 3435 C>T genotype was determined by polymerase chain reaction. RESULTS FLV concentration-to-dose ratio was significantly different among 3435 C>T genotype groups at the 200 mg/d dose (P = 0.019). A post-hoc analysis revealed that FLV concentration-to-dose ratio was significantly higher in the TT genotype group as compared with the CC genotype group at the 200 mg/d dose (median value of concentration-to-dose ratio (ng/mL)/(mg/d), 0.861 vs 0.434, P = 0.026). FLV concentration-to-dose ratio was significantly higher in the CT + TT genotype group than the CC genotype group at the 200 mg/d dose (median value of concentration-to-dose ratio (ng/mL)/(mg/d), 0.618 vs 0.434, P = 0.031). At 50, 100, and 150 mg/d dose, FLV concentration-to-dose ratios were not significantly different among 3435 C>T genotype groups. At 50, 100, and 150 mg/d dose, no significant differences were found in FLV concentration-to-dose ratios between the CT + TT genotype group and CC genotype group. CONCLUSIONS This study suggests that pharmacokinetics of FLV depend on ABCB1 gene polymorphism only at the 200 mg/d dose.

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

Objectives There are few reports regarding quetiapine (QTP)-related QT prolongation. We examined the change in QT interval after switching from aripiprazole (ARP), olanzapine (OLZ), or risperidone (RIS) to QTP. Methods Twenty subjects treated with ARP, OLZ, or RIS were enrolled in the study. Following baseline assessments, which included QT interval and electrolytes, these three drugs were switched to QTP for each subject. The same parameters were evaluated following a switch to QTP. Results All 20 patients who had been treated with ARP, OLZ, or RIS were successfully switched to QTP. Significant increases were observed in the total mean corrected QT (QTc) interval after switching (p = 0.014). The coefficient of variation for the extent of change in QTc interval was 1.66. The mean QTc with ARP treatment was significantly increased after QTP treatment (p = 0.004). Conclusions Quetiapine might have a greater effect on QTc interval than other second-generation antipsychotics. However, because there was a considerable variability in the extent of QTc prolongation after switch to QTP, further studies are required to clarify the effect of QTP on QTc interval. Copyright © 2012 John Wiley & Sons, Ltd.

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 The prevalence of diabetes in patients with schizophrenia is 2- to 3-fold higher than in the general population. Glucose abnormalities were detected in 11.9% of Japanese schizophrenic patients in a recent cross-sectional study that included fasting glucose monitoring. However, detailed studies of glucose intolerance using the glucose tolerance test have been limited in Japanese patients with schizophrenia. We investigated the prevalence of abnormal glucose tolerance after glucose loading among Japanese inpatients with schizophrenia, with normal fasting glucose levels. Method A total of 258 inpatients with schizophrenia participated in this study after giving their written informed consent. A 75-g oral glucose tolerance test was conducted in the morning after a 12-hour overnight fast. Results Among patients with normal fasting glucose, 81.3% had normal glucose tolerance, 17.3% had impaired glucose tolerance, and 1.3% were diagnosed with diabetes. Conclusions This study showed that the frequency of impaired glucose tolerance in patients with schizophrenia with normal fasting glucose levels might be higher than in the general population. Careful monitoring and screening of patients with schizophrenia for abnormal glucose metabolism might therefore be necessary.

We examined sex differences in the effect of olanzapine (OLZ), risperidone (RIS), aripiprazole (ARP), or quetiapine (QTP) on mean corrected QT (QTc) intervals among 222 patients with schizophrenia.Subjects were patients with schizophrenia who were treated with either OLZ (n = 69), RIS (n = 60), ARP (n = 62), or QTP (n = 31). Electrocardiographic measurements were conducted, and the QT interval was corrected using Bazett's correction formula.The mean QTc interval of the QTP group was significantly longer than that of the RIS group (p = 0.002) or ARP group (p = 0.029). The mean QTc interval of the OLZ group was also significantly longer than that of the RIS group (p = 0.006). In female participants, the difference in the mean QTc interval among the four second-generation antipsychotic (SGA) groups was statistically significant (p = 0.002), whereas in male patients, there was no significant difference in the mean QTc interval among the four SGA groups. Post hoc analyses showed that sex differences in QTc interval were observed only in OLZ treatment group (p = 0.007).To our knowledge, this is the first study to demonstrate sex differences in the effect of four SGAs on the QTc interval.

In this chapter we would like to discuss a generalization of Lefschetz elements for an Artinian local ring to study the Jordan decomposition of a general element. The point of departure for us is Theorem 5.1 due to D. Rees. Several results from Chap. 6 (e.g., stable ideals, Borel fixed ideals, gin(I), etc) are needed at a few points in Chap. 5.

The Lefschetz property originates in the Hard Lefschetz Theorem for compact Kahler manifolds, so it is natural that some results discussed in the former chapters have geometric backgrounds. For example, Corollary 4.17 on the flat extension can be understood from the cohomology ring of projective space bundles in a geometric setting.

The purpose of this chapter is to illustrate a role played by the SLP in connection with the theory of Artinian rings and the Schur–Weyl duality. We assume that the reader is familiar with commutative algebra but perhaps without knowledge of representation theory, but we are hopeful that the expert in representation theory may also find the following sections of interest.

The main result of this chapter is Theorem 4.10. This may be regarded as a generalization of Theorem 3.34 which states that the SLP is preserved by tensor products. Using the main theorem, we give some examples of complete intersections with the strong Lefschetz property.