Bounds for traces in complete intersections and degrees in the Nullstellensatz

In this paper we obtain an effective Nullstellensatz using quantitative considerations of the classical duality theory in complete intersections. Letk be an infinite perfect field and let f₁,...,f n–rk[X₁,...,X_n] be a regular sequence with d:=max_j deg f_j. Denote byA the polynomial ringk [X₁,..., X_r] and byB the factor ring k[X₁,...,X_n]/(f₁,...,f_n r); assume that the canonical morphism AB is injective and integral and that the Jacobian determinant with respect to the variables X_r+1,...,X_n is not a zero divisor inB. Let finally B^*:=Hom_A(B, A) be the generator of B^* associated to the regular sequence.We show that for each polynomialf the inequality deg (¯f) dⁿ r(+1) holds (¯fdenotes the class off inB and is an upper bound for (n–r)d and degf). For the usual trace associated to the (free) extensionA B we obtain a somewhat more precise bound: deg Tr(¯f) dⁿ r degf. From these bounds and Bertini's theorem we deduce an elementary proof of the following effective Nullstellensatz: let f₁,..., f_s be polynomials in k[X₁,...,X_n] with degrees bounded by a constant d2; then 1 (f₁,..., f_s) if and only if there exist polynomials p₁,..., p_sk[X₁,..., X_n] with degrees bounded by 4n(d+ 1)ⁿ such that 1=_ip_if_i. in the particular cases when the characteristic of the base fieldk is zero ord=2 the sharper bound 4ndⁿ is obtained.Partially supported by UBACYT and CONICET (Argentina)     

Magnetotransport properties of Zn90Mn7.5Cu2.5O100 films

Zn₉₀Mn_7.5Cu_2.5O₁₀₀ films have been prepared on a-plane sapphire substrates by pulsed laser deposition. Paramagnetism mainly caused by Mn²⁺ ions was observed in the films from room temperature down to 2 K. Magnetotransport properties (magnetoresistance (MR) and Hall effect) were studied from 5 K to 290 K up to a field of 6 T. Negative MR was observed at temperature above 100 K. Low field positive MR and high field negative MR was observed at 5 K. Clear anomalous Hall effect with a kink at low field was observed below 20 K, indicating that there exist two different scattering mechanisms for the Mn²⁺ and Cu²⁺ ions.     

Piezoelectricity and carrier dynamics in In0·2Ga0·8As/GaAs single quantum wells grown on (n11)A-oriented GaAs (n=1, 2, 3)

Temporal variations of the photoluminescence (PL) peak wavelength due to screening of the piezoelectric field by photogenerated carriers are observed in ln_0·2Ga_0·8As/GaAs single quantum wells grown on (n11)A-oriented substrates (n=1, 2, 3) by using time-resolved PL spectroscopy. The partial screening of the piezoelectric field shifts the PL peak to shorter wavelengths. The subsequent decrease of the photogenerated carriers by recombination produces a redshift of the PL peak, which is explained using a model that fits successfully the experimental results.     

In hemodialysis, adiponectin, and pro-brain natriuretic peptide levels may be subjected to variations in body mass index

Adiponectin exerts cardiovascular protective actions, although some studies have shown the opposite. In hemodialysis, obese subjects display lower mortality rates despite hypoadiponectinemia, while higher adiponectin concentrations correlate with an elevated cardiovascular risk in nonobese subjects. The aim of the study is to suggest that adiponectin level variations are associated with differences in the body mass index (BMI). The interplay between adiponectin and pro-brain natriuretic peptide (Pro-BNP) levels may vary according to body fat mass. Fifty-two chronic hemodialysis patients were divided into three groups. Group A, BMI<25 (n=20); Group B, BMI 25 to 30 (n=21), and Group C, BMI>30 (n=11). Diabetics: Group A 10%; Group B 6 29%; Group C 55%, P=0.027. Determinations: Adiponectin, Pro-BNP, insulin, insulin resistance (HOMA), troponin T, nutritional status, ultrafiltration rates, C-reactive protein (CRP), vascular accesses, and echocardiography. Group A: adiponectinemia positively and significantly correlated with Pro-BNP, CRP, and troponin T. As BMI increased, adiponectin, Pro-BNP, and malnutrition significantly decreased, while insulin, HOMA, and ultrafiltration rates significantly increased. Cardiac restriction was significantly higher in obese patients. In all groups, Pro-BNP and troponin T displayed a strong positive correlation. In low-BMI subjects, high Pro-BNP and adiponectin, low myocardial restriction, and worse nutritional status were prevalent. In obesity, hypoadiponectinemia stimulates cardiac remodeling, cardiac hypertrophy, and decreased stretching, rendering Pro-BNP levels low despite high ultrafiltration rates. Thus, adiponectin correlates inversely with BMI, probably playing different cardiovascular roles as BMI changes.