Parametric harmonic-to-fundamental ratio contrast echocardiography: a novel approach to identification and accurate measurement of left ventricular area under variable levels of ultrasound signal attenuation

Objectives

We introduced a harmonic-to-fundamental ratio (HFR) of the radiofrequency (RF) signals that reduces confounding effects of attenuation. We studied whether HFR analysis of RF signals received from contrast microbubbles allows accurate measurement of the left ventricular (LV) cavity area under varying levels of attenuation.

Background

Attenuation is a fundamental problem in ultrasound imaging and limits the use of clinical echocardiography.

Methods

RF data from short axis systolic and diastolic scans were obtained from 14 open-chest dogs following left-atrial bolus of Optison. Attenuation was induced by interposed silicone pads calibrated to induce 7 dB or 14 dB reductions of the backscattered RF signal. RF images were reconstructed from the RF signals, HFR values calculated for each image pixel for 0 dB, 7 dB and 14 dB attenuation conditions, and LV area obtained by summation of “LV cavity pixels”. A reference LV cavity area was obtained from endocardial border tracings in enhanced scans by experts.

Results

Correlation of the HFR-defined and reference areas at systole was R = 0.95, R = 0.94, and R = 0.91 for 0 dB, 7 dB and 14 dB levels of attenuation, respectively, and at diastole was R = 0.95 for 0 dB, 7 dB and 14 dB levels of attenuation. The mean difference from both systolic and diastolic values was <1.45 cm² (i.e. negligible) in all attenuation settings.

Conclusion

Our novel HFR method supports precise measurement of the LV cavity area in contrast images with simulated high attenuation of ultrasound signals.     

Quantification of Gd-DTPA concentration in neuroimaging using T₁3D MP-RAGE sequence at 3.0 T

Purpose

To propose a simple and accurate quantitative method based on the linear relationship between magnetic resonance (MR) signal enhancement (ΔSI=SI_postcontrast−SI_precontrast) and gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) concentration (C) by using T₁-weighted three-dimensional magnetization-prepared rapid acquisition gradient-echo (T₁ 3D MP-RAGE) sequence for the in vivo measurement of Gd-DTPA concentration in real-time neuroimaging at 3.0 T.

Methods

Phantom experiment was carried out to study the linear fitting of signal intensity change vs. Gd-DTPA concentration (ΔSI-C) curve. A goodness-of-fit test was performed to compare the accuracy between the proposed method and the conventional method based on longitudinal relaxation rate (R₁=1/T₁) measurement. The influences on the goodness of fit (R²) and the signal-to-noise ratio (SNR) by sequence parameters were explored. Six human subjects with different brain tumors, who underwent a Gd-DTPA-enhanced MRI, were enrolled for in vivo application of the novel method.

Results

A good linear relationship between ΔSI and Gd-DTPA concentration existed over the concentration range of 0-1 mM (R²=0.985). The linearity of the ΔSI-C curve was as good as that of the 1/T₁-C curve (R²=0.988). Concentrations calculated by both methods had a strong correlation (R²=0.920). An improved linearity of the ΔSI-C curve and an increased SNR can be achieved using sequences with a shorter inversion time (TI) and a higher flip angle. The concentration range of Gd-DTPA in human brain tumors was within the quantitative scope of 0-1 mM.

Conclusions

The proposed quantitative method based on ΔSI measurement is accurate and applicable for real-time neuroimaging at 3.0 T.     

In vitro comparative study of vibro-acoustography versus pulse-echo ultrasound in imaging permanent prostate brachytherapy seeds

Background

Permanent prostate brachytherapy (PPB) is a common treatment for early stage prostate cancer. While the modern approach using trans-rectal ultrasound guidance has demonstrated excellent outcome, the efficacy of PPB depends on achieving complete radiation dose coverage of the prostate by obtaining a proper radiation source (seed) distribution. Currently, brachytherapy seed placement is guided by trans-rectal ultrasound imaging and fluoroscopy. A significant percentage of seeds are not detected by trans-rectal ultrasound because certain seed orientations are invisible making accurate intra-operative feedback of radiation dosimetry very difficult, if not impossible. Therefore, intra-operative correction of suboptimal seed distributions cannot easily be done with current methods. Vibro-acoustography (VA) is an imaging modality that is capable of imaging solids at any orientation, and the resulting images are speckle free.

Objective and methods

The purpose of this study is to compare the capabilities of VA and pulse-echo ultrasound in imaging PPB seeds at various angles and show the sensitivity of detection to seed orientation. In the VA experiment, two intersecting ultrasound beams driven at f₁ = 3.00 MHz and f₂ = 3.020 MHz respectively were focused on the seeds attached to a latex membrane while the amplitude of the acoustic emission produced at the difference frequency 20 kHz was detected by a low frequency hydrophone.

Results

Finite element simulations and results of experiments conducted under well-controlled conditions in a water tank on a series of seeds indicate that the seeds can be detected at any orientation with VA, whereas pulse-echo ultrasound is very sensitive to the seed orientation.

Conclusion

It is concluded that vibro-acoustography is superior to pulse-echo ultrasound for detection of PPB seeds.     

Differentiation between intra-axial metastatic tumor progression and radiation injury following fractionated radiation therapy or stereotactic radiosurgery using MR spectroscopy, perfusion MR imaging or volume progression modeling

Objective

To determine the accuracy of magnetic resonance spectroscopy (MRS), perfusion MR imaging (MRP), or volume modeling in distinguishing tumor progression from radiation injury following radiotherapy for brain metastasis.

Methods

Twenty-six patients with 33 intra-axial metastatic lesions who underwent MRS (n=41) with or without MRP (n=32) after cranial irradiation were retrospectively studied. The final diagnosis was based on histopathology (n=4) or magnetic resonance imaging (MRI) follow-up with clinical correlation (n=29). Cho/Cr (choline/creatinine), Cho/NAA (choline/N-acetylaspartate), Cho/nCho (choline/contralateral normal brain choline) ratios were retrospectively calculated for the multi-voxel MRS. Relative cerebral blood volume (rCBV), relative peak height (rPH) and percentage of signal-intensity recovery (PSR) were also retrospectively derived for the MRPs. Tumor volumes were determined using manual segmentation method and analyzed using different volume progression modeling. Different ratios or models were tested and plotted on the receiver operating characteristic curve (ROC), with their performances quantified as area under the ROC curve (AUC). MRI follow-up time was calculated from the date of initial radiotherapy until the last MRI or the last MRI before surgical diagnosis.

Results

Median MRI follow-up was 16 months (range: 2-33). Thirty percent of lesions (n=10) were determined to be radiation injury; 70% (n=23) were determined to be tumor progression. For the MRS, Cho/nCho had the best performance (AUC of 0.612), and Cho/nCho >1.2 had 33% sensitivity and 100% specificity in predicting tumor progression. For the MRP, rCBV had the best performance (AUC of 0.802), and rCBV >2 had 56% sensitivity and 100% specificity. The best volume model was percent increase (AUC of 0.891); 65% tumor volume increase had 100% sensitivity and 80% specificity.

Conclusion

Cho/nCho of MRS, rCBV of MRP, and percent increase of MRI volume modeling provide the best discrimination of intra-axial metastatic tumor progression from radiation injury for their respective modalities. Cho/nCho and rCBV appear to have high specificities but low sensitivities. In contrast, percent volume increase of 65% can be a highly sensitive and moderately specific predictor for tumor progression after radiotherapy. Future incorporation of 65% volume increase as a pretest selection criterion may compensate for the low sensitivities of MRS and MRP.     

Low-temperature growth of ZnO nanorods on PET fabrics with two-step hydrothermal method

An effective low-temperature growth method to fabricate hexagonally oriented ZnO nanorod arrays onto PET fabrics is reported. The effect of substrate pre-treatment and C₆H₁₂N₄ concentration on the structure of ZnO nanorod arrays were investigated in details by X-ray diffraction (XRD), FE-SEM and ultraviolet protection factor (UPF). The results show that substrate pre-treatment, C₆H₁₂N₄ concentration indeed have great influence on the growth of ZnO nanorod arrays. It is indispensable to introduce a ZnO seed layer on the substrate and under growth condition of n(C₆H₁₂N₄):n[Zn(NO₃)₂] = 1:1, T = 90 °C, t = 3 h, the well-aligned ZnO nanorod arrays with 40-50 nm in diameter and 300-400 nm in length were achieved on the pre-treated PET fabrics. The ZnO nanorods grown on PET fabrics possessed an ultrahigh ultraviolet protection factor of 480.52 in this study, indicating an excellent protection against ultraviolet radiation in comparison with the untreated PET fabrics.     

Gas challenge-blood oxygen level-dependent (GC-BOLD) MRI in the rat Novikoff hepatoma model

Purpose

The purpose of the study was to investigate the relationship between gas challenge-blood oxygen level-dependent (GC-BOLD) response angiogenesis and tumor size in rat Novikoff hepatoma model.

Materials and Methods

Twenty adult male Sprague-Dawley rats (weighting 301-325 g) were used for our Animal Care and Use Committee-approved experiments. N1-S1 Novikoff hepatomas were grown in 14 rats with sizes ranging from 0.42 to 2.81 cm. All experiments were performed at 3.0 T using a custom-built rodent receiver coil. A multiple gradient-echo sequence was used for R2^? measurements, first during room air (78% N₂/20% O₂) breathing and then after 10 min of carbogen (95% O₂/5% CO₂) breathing. After image acquisition, rats were euthanized, and the tumors were harvested for histological evaluation.

Results

The R2^? change between air and carbogen breathing for small hepatomas was positive; R2^? changes changed to negative values for larger hepatomas. We found a significant positive correlation between tumor R2^? change and tumor microvessel density (MVD) (r=0.798, P=.001) and a significant inverse correlation between tumor R2^? change and tumor size (r=−0.840, P<.0001).

Conclusions

GC-BOLD magnetic resonance imaging measurements are well correlated to MVD levels and tumor size in the N1-S1 Novikoff hepatoma model; GC-BOLD measurements may serve as noninvasive biomarkers for evaluating angiogenesis and disease progression and/or therapy response.     

The oxidation of fullerenes (C<Subscript>60</Subscript>, C<Subscript>70</Subscript>) with various oxidants under ultrasonication

The reaction of C₆₀, under ultrasonication, with various oxidants, such as 3-chloroperoxy benzoic acid (Fluka 99%), 4-methyl morpholine N-oxide (Aldrich 97%), chromium (VI) oxide (Aldrich 99.9%), and the oxone® monopersulfate compound, causes the oxidation of fullerenes at room temperature. The FAB-MS spectra and HPLC profile confirmed that the products of fullerene oxidation were [C₆₀(O)_n] (n=1～3 or n=1). C₇₀ also reacted, under ultrasonication, with various oxidants, but the reaction rate of C₇₀ was lower than that of C₆₀.     

Distribution of late gadolinium enhancement in end-stage hypertrophic cardiomyopathy and dilated cardiomyopathy: Differential diagnosis and prediction of cardiac outcome

Background

The prognostic implications of late gadolinium enhancement (LGE) have been evaluated in ischemic and non-ischemic cardiomyopathies. The present study analyzed LGE distribution in patients with end-stage hypertrophic cardiomyopathy (ES-HCM) and with dilated cardiomyopathy (DCM), and tried to identify high risk patients in DCM.

Methods

Eleven patients with ES-HCM and 72 with DCM underwent cine- and LGE-cardiac magnetic resonance and ultrasound cardiography. The patient outcome was analyzed retrospectively for 5 years of follow-up.

Results

LGE distributed mainly in the inter-ventricular septum, but spread more diffusely into other left ventricular segments in patients with ES-HCM and in a certain part of patients with DCM. Thus, patients with DCM can be divided into three groups according to LGE distribution; no LGE (n = 24), localized LGE (localized at septum, n = 36), and extensive LGE (spread into other segments, n = 12). Reverse remodeling occurred after treatment in patients with no LGE and with localized LGE, but did not in patients with extensive LGE and with ES-HCM. The event-free survival rate for composite outcome (cardiac death, hospitalization for decompensated heart failure or ventricular arrhythmias) was lowest in patients with extensive LGE (92%, 74% and 42% in no LGE, localized LGE, and extensive LGE, p = 0.02 vs. no LGE), and was comparable to that in patients with ES-HCM (42%).

Conclusions

In DCM, patients with extensive LGE showed no functional recovery and the lowest event-free survival rate that were comparable to patients with ES-HCM. The analysis of LGE distribution may be valuable to predict reverse remodeling and to identify high-risk patients.     

Quantitative assessment of regional systolic and diastolic functions and temporal heterogeneity of myocardial contraction in patients with myocardial infarction using cine magnetic resonance imaging and Fourier fitting

Purpose

The objective of this study is to determine regional left ventricle (LV) function and temporal heterogeneity of LV wall contraction by analyzing regional time–volume curve (TVC) after Fourier fitting and to assess altered systolic and diastolic functions and temporal indices of myocardial contraction in infarcted segments in comparison with noninfarcted myocardium in patients with myocardial infarction (MI).

Methods

Steady-state cine magnetic resonance (MR) and late gadolinium-enhanced (LGE) MR images were acquired using a 1.5-T MR system in 60 patients with MI. Regional LV function was determined by analyzing regional TVC in 16 segments. The fitted regional TVC was generated by Fourier curve fitting with five harmonics. Regional LV ejection fraction (EF), peak ejection rate (PER), peak filling rate (PFR), time to end-systole and time to peak filling (TPF) were determined from TVC and the first derivative curve.

Results

On LGE MR imaging (MRI), MI was observed in 307 of 960 segments (32.0%). Regional EF and PER averaged in LGE segments were 49.3±14.5% and 2.83±0.65 end-diastolic volume (EDV)/s, significantly lower than those in normal segments (66.7±11.9% and 3.63±0.60 EDV/s, P<.001 and P<.01, respectively). In addition, regional PFR, an index of diastolic function, was significantly reduced in LGE segments (1.94±0.54 vs. 2.86±0.68 EDV/s, P<.01). Time to end-systole and TPF were significantly greater in LGE segments (380.2±57.6 and 169.3±45.4 ms) than in normal segments (300.9±55.1 and 132.3±43.0 ms, P<.01 and P<.01, respectively).

Conclusions

Analysis of regional TVC on cine MRI after Fourier fitting allows quantitative assessment of regional systolic and diastolic LV functions and temporal heterogeneity of LV wall contraction in patients with MI.     

Laser ablation time-of-flight mass spectrometry (LA-TOF-MS) of “nitrogen doped diamond-like carbon (DLN) nano-layers”

Nitrogen-doped diamond-like carbon (DLC) layers (a-C:H:N, N-DLC or DLN) were prepared by the plasma-enhanced chemical vapor deposition (PECVD) technique, using a RF capacitive discharge (13.56 MHz), at low pressures (20 Pa), produced from a mixture of methane, nitrogen and hexamethyldisiloxane (HMDSO), deposited on single-crystalline silicon wafers placed on steel samples. The films, of differing deposition times, were subjected to laser ablation time-of-flight (LA-TOF) mass spectrometric measurements, using different commercial instrumentation to characterize their structures. The analysis of mass spectra was made and the following positively singly charged species were detected and identified: C_n⁺ (n=4–30), Si_n⁺ (n=2, 3), Si_nH⁺ (n=2, 3), SiOK⁺, Si₃H₄⁺, Si₂N⁺, Si₂NH₂⁺, and Si₃C⁺. The later three species could reflect the presence of nitrogen–silica and carbon–silica chemical bonds in the structure of the DLN layer. The stoichiometry of all species was confirmed by isotopic pattern simulation. In the negative detection mode, the C_n⁻ (n=2–12) clusters were observed. The findings are discussed in the light of the current research concerning analysis of the DLN thin layers and it is concluded that namely Si₂N⁺, Si₂NH₂⁺ and Si₃C⁺ species are reflecting the chemical structure of the DLN layer. LA-TOF-MS was found useful supplementary method for the characterization of DLN nano-layers.     

Detection of small intrahepatic metastases of hepatocellular carcinomas using diffusion-weighted imaging: comparison with conventional dynamic MRI

Purpose

The purpose of our study was to compare diffusion-weighted MR imaging (DWI) with conventional dynamic MRI in terms of the assessment of small intrahepatic metastases from hepatocellular carcinoma (HCC).

Materials and Methods

In 24 patients with multifocal, small (≤2 cm) intrahepatic metastatic foci of advanced HCC, a total of 134 lesions (≤1 cm, n=81; >1 cm, n=53) were subjected to a comparative analysis of hepatic MRI including static and gadopentetate dimeglumine-enhanced dynamic imaging, and DWI using a single-shot spin-echo echo-planar MRI (b values=50, 400 and 800 s/mm²), by two independent reviewers.

Results

A larger number of the lesions were detected and diagnosed as intrahepatic metastases on DWI [Reviewer 1, 121 (90%); Reviewer 2, 117 (87%)] than on dynamic imaging [Reviewer 1, 107 (80%); Reviewer 2, 105 (78%)] (P<.05). For the 81 smaller lesions (≤1 cm), DWI was able to detect more lesions than dynamic imaging [Reviewer 1, 68 (84%) vs. 56 (69%), P=.008; Reviewer 2, 65 (80%) vs. 55 (68%), P=.031], but there was no statistically significant difference between the two image sets for larger (>1 cm) lesions.

Conclusion

Due to its higher detection rate of subcentimeter lesions, DWI could be considered complementary to dynamic MRI in the diagnosis of intrahepatic metastases of HCCs.     

Phantom investigation of phase-inversion-based dual-frequency excitation imaging for improved contrast display

Objective

The goal of this work is to examine the effects of pulse-inversion (PI) technique in combination with dual-frequency (DF) excitation method to separate the high-order nonlinear responses from microbubble contrast agents for improvement of image contrast. DF excitation method has been previously developed to induce the low-frequency ultrasound nonlinear responses from bubbles by using the composition of two high-frequency sinusoids (f₁ and f₂).

Motivation

Although the simple filtering was conventionally utilized to provide signal separation, the PI approach is better in the sense that it minimizes the mutual interferences among these high-order nonlinear responses in the presence of spectral overlap. The novelty of the work is that, in addition to the common PI summation, the PI subtraction was also applied in DF excitation method.

Methods

DF excitation pulses having an envelope frequency of 3 MHz (i.e., f₁ = 8.5 MHz and f₂ = 11.5 MHz) with pulse lengths of 3-10 μs and the pressure amplitudes from 0.5 to 1.5 MPa were used to interrogate the nonlinear responses of SonoVue™ microbubbles in the phantom experiments. The high-order nonlinear responses in the DF excitation were extracted for contrast imaging using PI summation for even-order nonlinear components or PI subtraction for odd-order nonlinear ones.

Results

Our results indicated that, as compared to the conventional filtering technique, the PI processing effectively increases the contrast-to-tissue ratio (CTR) of the third-order nonlinear response at 5.5 MHz and the fourth-order nonlinear response at 6 MHz by 2-5 dB. For these high-order nonlinear components, the CTR increase varies with the transmission pressures from 0.5 to 1.5 MPa due to the microbubbles’ displacement induced by the radiation force of DF excitation.

Conclusions

For DF excitation technique, the PI processing can help to extract either the odd-order or the even-order nonlinear components for higher CTR estimates.     

Ultrasound induces cellular destruction of nasopharyngeal carcinoma cells in the presence of curcumin

Objectives

Curcumin, a natural pigment from the traditional Chinese herb, has shown promise as an efficient enhancer of ultrasound. The present study aims to investigate ultrasound-induced cellular destruction of nasopharyngeal carcinoma cells in the presence of curcumin in vitro.

Methods

Nasopharyngeal carcinoma cell line CNE2 cells were incubated by 10 μm curcumin and then were treated by ultrasound for 8 s at the intensity of 0.46 W/cm². Cytotoxicity was evaluated using MTT assay and light microscopy. Mitochondrial damage was analyzed using a confocal laser scanning microcopy with Rhodamine 123 and ultrastructural changes were observed using a transmission electron microscopy (TEM).

Results

MTT assay showed that cytotoxicity induced by ultrasound treatment alone and curcumin treatment alone was 18.16 ± 2.37% and 24.93 ± 8.30%, respectively. The cytotoxicity induced by the combined treatment of ultrasound and curcumin significantly increased up to 86.67 ± 7.78%. TEM showed that microvillin disappearance, membrane blebbing, chromatin condensation, swollen mitochondria, and mitochondrial myelin-like body were observed in the cells treated by ultrasound and curcumin together. The significant collapse of mitochondrial membrane potential (MMP) was markedly observed in the CNE2 cells after the combined treatment of curcumin and ultrasound.

Conclusions

Our findings demonstrated that ultrasound sonication in the presence of curcumin significantly killed the CNE2 cells and induced ultrastructural damage and the dysfunction of mitochondria, suggesting that ultrasound treatment remarkably induced cellular destruction of nasopharyngeal carcinoma cells in the presence of curcumin.     

Bounds on the number of eigenvalues of the Schrödinger operator

Inequalities on eigenvalues of the Schrödinger operator are re-examined in the case of spherically symmetric potentials. In particular, we obtain:

1. A connection between the moments of order (n ? 1)/2 of the eigenvalues of a one-dimensional problem and the total number of bound statesN _n, inn space dimensions;
2. optimal bounds on the total number of bound states below a given energy in one dimension;
3. alower bound onN ₂;
4. a self-contained proof of the inequality for α ≧ 0,n ≧ 3, leading to the optimalC ₀₄,C ₃;
5. solutions of non-linear variation equations which lead, forn ≧ 7, to counter examples to the conjecture thatC _0n is given either by the one-bound state case or by the classic limit; at the same time a conjecture on the nodal structure of the wave functions is disproved.

     

Dark matter from the SU(4) model

The left-right symmetric Pati-Salam model of the unification of quarks and leptons is based on the SU(4) and SU(2)×SU(2) symmetry groups. These groups are naturally extended to include the classification of families of quarks and leptons. We assume that the family group (the group which unites the families) is also the SU(4) group. The properties of the fourth generation of fermions are the same as those of the ordinary-matter fermions in the first three generations except for the family charge of the SU(4)_F group: F=(1/3, 1/3, 1/3, ?1), where F=1/3 for fermions of ordinary matter and F=?1 for the fourth-generation fermions. The difference in F does not allow mixing between ordinary and fourth-generation fermions. Because of the conservation of the Fcharge, the creation of baryons and leptons in the process of electroweak baryogenesis must be accompanied by the creation of fermions of the fourth generation. As a result, the excess n _B of baryons over antibaryons leads to the excess n_4ν=N?N? of neutrinos over antineutrinos in the fourth generation with n_4ν=n _B . This massive neutrino may form nonbaryonic dark matter. In principle, the mass density of the fourth neutrino n_4νm _N in the Universe can make the main contribution to dark matter, since the lower bound on the neutrino mass m _N from the data on decay of the Z bosons is m _N <m _Z /2. The straightforward prediction of this model leads to the amount of cold dark matter relative to baryons, which is an order of magnitude higher than allowed by observations. This inconsistency may be avoided by nonconservation of the F charge.     

Stoichiometric synthesis of fullerene compounds with lithium and sodium and analysis of their IR and EPR spectra

A modified method is proposed for preparing fullerene compounds with alkali metals in a solution. The compounds synthesized have the general formula Me _n C₆₀(THF)_x, where Me = Li or Na; n=1–4, 6, 8, or 12; and THF = tetrahydrofuran. The use of preliminarily synthesized additives MeC₁₀H₈ makes it possible to prepare fullerene compounds with an exact stoichiometric ratio between C ₆₀ ^n? and Me ⁺. The IR and EPR spectra of the compounds prepared are analyzed and compared with the spectra of their analogs available in the literature. The intramolecular modes T _u (1)-T _u (4) for the C ₆₀ ^n? anion are assigned. The splitting of the T _u (1) mode into a doublet at room temperature for Me _n C₆₀(THF)_x (n=1, 2, 4) compounds indicates that the fullerene anion has a distorted structure. An increase in the intensity of the T _u (2) mode, a noticeable shift of the T _u (4) mode toward the long-wavelength range, and an anomalous increase in the intensity of the latter mode for the Li₃C₆₀(THF)_x complex suggest that, in the fullerene anion, the coupling of vibrational modes occurs through the charge-phonon mechanism. The measured EPR spectra of lithium-and sodium-containing fullerene compounds are characteristic of C ₆₀ ^? anions. The g factors for these compounds are almost identical and do not depend on temperature. The g factor for the C ₆₀ ^n? anion depends on the nature of the metal and differs from the g factor for the C ₆₀ ^? anion.     

Gauge dependence of the effective action in multidimensional supergravities

The problem of gauge dependence of the effective action in multidimensional supergravities (SG) is investigated. As an example d=5 SGs are considered. The convenient gauge-dependent effective action (EA) and gauge-invariant Vilkovisky-De Witt EA in d=5, N=2, 4, 6, 8 SGs on the background R₄×S₁ with accuracy to linear curvature terms are obtained. The convenient three-gauge-parameter-dependent EA in d=5, N=2 gauged SG on the background R₄×S₁ is calculated. The Vilkovisky-De Witt EA in d=5 SGs on the background R₄×S₁ at non-zero temperature is also obtained.     

The crystal structure of (L-proline-L-alanine) copper (II)·2·5 H2O

The crystal and molecular structure of (L-proline-L-alanine) Cu·2·5 H₂O has been determined by the heavy atom method with 583 visually estimated reflexions and refined by full matrix least squares toR=0·101. The crystals are monoclinic witha=16·47 (3),b=7·74 (2),c=9·51 (3) Å andβ=109·7 (5)°; space groupC2;Z=4. The copper coordination is nearly square pyramidal with one water in the basal plane and another occupying the apical together with the aminoN, peptideN and the carboxylO of the dipeptide in the coordination. The Cu-peptide-Cu linkage isvia the hydrogen bonding between the water in the basal plane and the carbonyl O atom of the proline residue. One water is on the 2-fold axis.     

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Within the four-loop ε expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is supported by the estimate of critical dimensionality N _c ^C =1.445(20) obtained from six loops via the exact relation N _c ^C =1/2N _c ^R established for the complex and real hypercubic models.     

Nilpotent invariants in N=4 SYM

It is shown that there are no nilpotent invariants in N=4 analytic superspace for n≤4 points. It is argued that there is (at least) one such invariant for n=5 points which is not invariant under U(1)_Y. The consequences of these results are that the n=2 and 3 point correlation functions of the N=4 gauge-invariant operators which correspond to KK multiplets in AdS supergravity are given exactly by their tree level expressions, the 4 point correlation functions of such operators are invariant under U(1)_Y and correlation functions with n≥4 points have non-trivial dependence on the Yang-Mills coupling constant.