'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Time evolution of the Wigner function in discrete quantum phase space for a soluble quasi-spin model

The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wi:ner function is written for some chosen states associated to discrete angle and angular momentum variables, and the rime evolution is numerically calculated using the discrete von Neumnnn-Liouville equation. Direct evidences in the lime evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU(2)-based semiclassical continuous approach to the Lipkin model is also presented.

Modulation transfer function and optical quality after bilateral implantation of a+3.00 D versus a+4.00 D multifocal intraocular lens

PURPOSE: To determine whether the improvement in intermediate vision after bilateral implantation of an aspheric multifocal intraocular lens (IOL) with a +3.00 diopter (D) addition (add) occurs at the expense of optical quality compared with the previous model with a +4.00 D add. SETTING: Department of Ophthalmology, University of Sao Paulo, Sao Paulo, Brazil. DESIGN: Prospective randomized double-masked comparative clinical trial. METHODS: One year after bilateral implantation of Acrysof Restor SN6AD1 +3.00 D IOLs or Acrysof Restor SN6AD3 +4.00 D IOLs, optical quality was evaluated by analyzing the in vivo modulation transfer function (MTF) and point-spread function (expressed as Strehl ratio). The Strehl ratio and MTF curve with a 4.0 pupil and a 6.0 mm pupil were measured by dynamic retinoscopy aberrometry. The uncorrected and corrected distance visual acuities at 4 m, uncorrected and distance-corrected near visual acuities at 40 cm, and uncorrected and distance-corrected intermediate visual acuities at 50 cm, 60 cm, and 70 cm were measured. RESULTS: Both IOL groups comprised 40 eyes of 20 patients. One year postoperatively, there were no statistically significant between-group differences in the MTF or Strehl ratio with either pupil size. There were no statistically significant between-group differences in distance or near visual acuity. Intermediate visual acuity was significantly better in the +3.00 D IOL group. CONCLUSION: Results indicate that the improvement in intermediate vision in eyes with the aspheric multifocal +3.00 D add IOL occurred without decreasing optical quality over that with the previous version IOL with a +4.00 D add.

Atorvastatin Prevents the Downregulation of Aquaporin-2 Receptor After Bilateral Ureteral Obstruction and Protects Renal Function in a Rat Model

OBJECTIVE To assess the effects of atorvastatin (ATORV) on renal function after bilateral ureteral obstruction (BUO), measuring inulin clearance and its effect on renal hemodynamic, filtration, and inflammatory response, as well as the expression of Aquaporin-2 (AQP2) in response to BUO and after the release of BUO. METHODS Adult Munich-Wistar male rats were subjected to BUO for 24 hours and monitored during the following 48 hours. Rats were divided into 5 groups: sham operated (n = 6); sham + ATORV (n = 6); BUO (n = 6); BUO + ATORV (10 mg/kg in drinking water started 2 days before BUO [n = 5]; and BUO + ATORV (10 mg/kg in drinking water started on the day of the release of BUO [n = 5]). We measured blood pressure (BP, mm Hg); inulin clearance (glomerular filtration rate [GFR]; mL/min/100 g); and renal blood flow (RBF, mL/min, by transient-time flowmeter). Inflammatory response was evaluated by histologic analysis of the interstitial area. AQP2 expression was evaluated by electrophoresis and immunoblotting. RESULTS Renal function was preserved by ATORV treatment, even if initiated on the day of obstruction release, as expressed by GFR, measured by inulin clearance. Relative interstitial area was decreased in both BUO + ATORV groups. Urine osmolality was improved in the ATORV-treated groups. AQP2 protein expression decreased in BUO animals and was reverted by ATORV treatment. CONCLUSION ATORV administration significantly prevented and restored impairment in GFR and renal vascular resistance. Furthermore, ATORV also improved urinary concentration by reversing the BUO-induced downregulation of AQP2. These findings have significant clinical implication in treating obstructive nephropathy. UROLOGY 80: 485.e15-485.e20, 2012. (c) 2012 Elsevier Inc.

Longterm peripheral baroreflex and chemoreflex function after bilateral eversion carotid endarterectomy

Introduction The “eversion” technique for carotid endarterectomy (e-CEA), that involves the transection of the internal carotid artery at the carotid bulb and its eversion over the atherosclerotic plaque, has been associated with an increased risk of postoperative hypertension possibly due to a direct iatrogenic damage to the carotid sinus fibers. The aim of this study is to assess the long-term effect of the e-CEA on arterial baroreflex and peripheral chemoreflex function in humans. Methods A retrospective review was conducted on a prospectively compiled computerized database of 3128 CEAs performed on 2617 patients at our Center between January 2001 and March 2006. During this period, a total of 292 patients who had bilateral carotid stenosis ≥70% at the time of the first admission underwent staged bilateral CEAs. Of these, 93 patients had staged bilateral e-CEAs, 126 staged bilateral s- CEAs and 73 had different procedures on each carotid. CEAs were performed with either the eversion or the standard technique with routine Dacron patching in all cases. The study inclusion criteria were bilateral CEA with the same technique on both sides and an uneventful postoperative course after both procedures. We decided to enroll patients submitted to bilateral e-CEA to eliminate the background noise from contralateral carotid sinus fibers. Exclusion criteria were: age >70 years, diabetes mellitus, chronic pulmonary disease, symptomatic ischemic cardiac disease or medical therapy with b-blockers, cardiac arrhythmia, permanent neurologic deficits or an abnormal preoperative cerebral CT scan, carotid restenosis and previous neck or chest surgery or irradiation. Young and aged-matched healthy subjects were also recruited as controls. Patients were assessed by the 4 standard cardiovascular reflex tests, including Lying-to-standing, Orthostatic hypotension, Deep breathing, and Valsalva Maneuver. Indirect autonomic parameters were assessed with a non-invasive approach based on spectral analysis of EKG RR interval, systolic arterial pressure, and respiration variability, performed with an ad hoc software. From the analysis of these parameters the software provides the estimates of spontaneous baroreflex sensitivity (BRS). The ventilatory response to hypoxia was assessed in patients and controls by means of classic rebreathing tests. Results A total of 29 patients (16 males, age 62.4±8.0 years) were enrolled. Overall, 13 patients had undergone bilateral e-CEA (44.8%) and 16 bilateral s-CEA (55.2%) with a mean interval between the procedures of 62±56 days. No patient showed signs or symptoms of autonomic dysfunction, including labile hypertension, tachycardia, palpitations, headache, inappropriate diaphoresis, pallor or flushing. The results of standard cardiovascular autonomic tests showed no evidence of autonomic dysfunction in any of the enrolled patients. At spectral analysis, a residual baroreflex performance was shown in both patient groups, though reduced, as expected, compared to young controls. Notably, baroreflex function was better maintained in e-CEA, compared to standard CEA. (BRS at rest: young controls 19.93 ± 2.45 msec/mmHg; age-matched controls 7.75 ± 1.24; e-CEA 13.85 ± 5.14; s-CEA 4.93 ± 1.15; ANOVA P=0.001; BRS at stand: young controls 7.83 ± 0.66; age-matched controls 3.71 ± 0.35; e-CEA 7.04 ± 1.99; s-CEA 3.57 ± 1.20; ANOVA P=0.001). In all subjects ventilation (VÝ E) and oximetry data fitted a linear regression model with r values > 0.8. Oneway analysis of variance showed a significantly higher slope both for ΔVE/ΔSaO2 in controls compared with both patient groups which were not different from each other (-1.37 ± 0.33 compared with -0.33±0.08 and -0.29 ±0.13 l/min/%SaO2, p<0.05, Fig.). Similar results were observed for and ΔVE/ΔPetO2 (-0.20 ± 0.1 versus -0.01 ± 0.0 and -0.07 ± 0.02 l/min/mmHg, p<0.05). A regression model using treatment, age, baseline FiCO2 and minimum SaO2 achieved showed only treatment as a significant factor in explaining the variance in minute ventilation (R2= 25%). Conclusions Overall, we demonstrated that bilateral e-CEA does not imply a carotid sinus denervation. As a result of some expected degree of iatrogenic damage, such performance was lower than that of controls. Interestingly though, baroreflex performance appeared better maintained in e-CEA than in s-CEA. This may be related to the changes in the elastic properties of the carotid sinus vascular wall, as the patch is more rigid than the endarterectomized carotid wall that remains in the e-CEA. These data confirmed the safety of CEA irrespective of the surgical technique and have relevant clinical implication in the assessment of the frequent hemodynamic disturbances associated with carotid angioplasty stenting.

Quantitative evaluation of visual function 12 months after bilateral implantation of a diffractive trifocal IOL

PURPOSE: To quantitatively evaluate visual function 12 months after bilateral implantation of the Physiol FineVision® trifocal intraocular lens (IOL) and to compare these results with those obtained in the first postoperative month. METHODS: In this prospective case series, 20 eyes of 10 consecutive patients were included. Monocular and binocular, uncorrected and corrected visual acuities (distance, near, and intermediate) were measured. Metrovision® was used to test contrast sensitivity under static and dynamic conditions, both in photopic and low-mesopic settings. The same software was used for pupillometry and glare evaluation. Motion, achromatic, and chromatic contrast discrimination were tested using 2 innovative psychophysical tests. A complete ophthalmologic examination was performed preoperatively and at 1, 3, 6, and 12 months postoperatively. Psychophysical tests were performed 1 month after surgery and repeated 12 months postoperatively. RESULTS: Final distance uncorrected visual acuity (VA) was 0.00 ± 0.08 and distance corrected VA was 0.00 ± 0.05 logMAR. Distance corrected near VA was 0.00 ± 0.09 and distance corrected intermediate VA was 0.00 ± 0.06 logMAR. Glare testing, pupillometry, contrast sensitivity, motion, and chromatic and achromatic contrast discrimination did not differ significantly between the first and last visit (p>0.05) or when compared to an age-matched control group (p>0.05). CONCLUSIONS: The Physiol FineVision® trifocal IOL provided satisfactory full range of vision and quality of vision parameters 12 months after surgery. Visual acuity and psychophysical tests did not vary significantly between the first and last visit.

Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\Rn)$, $1 \leq p < \infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\Rn)$, $0

Quantitative evaluation of visual function 12 months after bilateral implantation of a diffractive trifocal IOL

PURPOSE: To quantitatively evaluate visual function 12 months after bilateral implantation of the Physiol FineVision® trifocal intraocular lens (IOL) and to compare these results with those obtained in the first postoperative month. METHODS: In this prospective case series, 20 eyes of 10 consecutive patients were included. Monocular and binocular, uncorrected and corrected visual acuities (distance, near, and intermediate) were measured. Metrovision® was used to test contrast sensitivity under static and dynamic conditions, both in photopic and low-mesopic settings. The same software was used for pupillometry and glare evaluation. Motion, achromatic, and chromatic contrast discrimination were tested using 2 innovative psychophysical tests. A complete ophthalmologic examination was performed preoperatively and at 1, 3, 6, and 12 months postoperatively. Psychophysical tests were performed 1 month after surgery and repeated 12 months postoperatively. RESULTS: Final distance uncorrected visual acuity (VA) was 0.00 ± 0.08 and distance corrected VA was 0.00 ± 0.05 logMAR. Distance corrected near VA was 0.00 ± 0.09 and distance corrected intermediate VA was 0.00 ± 0.06 logMAR. Glare testing, pupillometry, contrast sensitivity, motion, and chromatic and achromatic contrast discrimination did not differ significantly between the first and last visit (p>0.05) or when compared to an age-matched control group (p>0.05). CONCLUSIONS: The Physiol FineVision® trifocal IOL provided satisfactory full range of vision and quality of vision parameters 12 months after surgery. Visual acuity and psychophysical tests did not vary significantly between the first and last visit.

Masticatory afficiency in denture wearers with bilateral balanced occlusion and canine guidance

The maintenance of masticatory function is especially important for patients wearing complete dentures due to their limitations. Thus, the bilateral balanced occlusal concept is used to achieve greater masticatory efficiency. However, a critical review of the literature reveals that there is not sufficient scientific evidence to support bilateral balanced occlusion as the most appropriate occlusal concept in complete dentures. Therefore, the aim of this study was to evaluate the masticatory efficiency in complete dentures wearers with bilateral balanced occlusion and canine guidance. A double-blinded controlled crossover clinical trial was conducted. The sample was composed by 24 edentulous patients who wore sets of complete dentures with both occlusal concepts during equal periods of 3 months. Objective data were collected through the masticatory efficiency test performed by the colorimetric method with the beads, in which capsules of a synthetic material enclosing fuchsine-containing granules were used. Subjective data were recorded by patient's ratings of their chewing function. No significant statistical difference was found for masticatory efficiency (p=0.095) between the two occlusal concepts studied. The results suggest that bilateral balanced occlusion does not improve the masticatory efficiency in complete denture wearers.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Mechanisms of substitution reactions on cyclometallated platinum(IV) complexes: "Quasi-labile" systems

The substitution reactions of SMe2 by phosphines (PMePh2, PEtPh2, PPh3, P(4-MeC6H4)(3), P(3-MeC6H4)(3), PCy3) on Pt-IV complexes having a cyclometalated imine ligand, two methyl groups in a cis-geometrical arrangement, a halogen, and a dimethyl sulfide as ligands, [Pt(CN)(CH3)(2)(X)(SMe2)], have been studied as a function of temperature, solvent, and electronic and steric characteristics of the phosphines and the X and CN ligands. In all cases, a limiting dissociative mechanism has been found, where the dissociation of the SMe2 ligand corresponds to the rate-determining step. The pentacoordinated species formed behaves as a true pentacoordinated Pt-IV compound in a steady-state concentration, given the solvent independence of the rate constant. The X-ray crystal structures of two of the dimethyl sulfide complexes and a derivative of the pentacoordinate intermediate have been determined. Differences in the individual rate constants for the entrance of the phosphine ligand can only be estimated as reactivity ratios. In all cases an effect of the phosphine size is detected, indicating that an associative step takes place from the pentacoordinated intermediate. The nature of the (CN) imine and X ligands produces differences in the dimethyl sulfide dissociation reactions rates, which can be quantified by the corresponding DeltaS double dagger values (72, 64, 48, 31, and 78 J K-1 mol(-1) for CN/X being C6H4CHNCH2C6H5/Br, C6H4CHNCH2-(2,4,6-(CH3)(3))C6H2/Br, C6H4CHNCH2C6H5/Cl, C6Cl4CHNCH2C6H5/Cl, and C6W4CH2NCHC6H5/ Pr, respectively). As a whole, the donor character of the coordinated C-aromatic and X atoms have the greatest influence on the dissociativeness of the rate-determining step.

Wavefront analysis and modulation transfer function of three multifocal intraocular lenses

Purpose: To evaluate wavefront performance and modulation transfer function (MTF) in the human eye aft er the implantation of diffractive or refractive multifocal intraocular lenses (IOLs). Materials and Methods: This was a prospective, interventional, comparative, nonrandomized clinical study. Uncorrected distance and near visual acuity, and wavefront analysis including MTF curves (iTrace aberrometer, Tracey Technologies, Houston, TX, USA) were measured in 60 patients aft er bilateral IOL implantation with 6 months of follow-up. Forty eyes received the diffractive ReSTOR (Alcon), 40 eyes received the refractive ReZoom (Advanced Medical Optics) and 40 eyes, the Tecnis ZM900 (Advanced Medical Optics). The comparison of MTF and aberration between the intraocular lenses was performed using analysis of variance (ANOVA), followed by the Dunn test when necessary. Results: The mean uncorrected distance visual acuity was similar in all three groups of multifocal IOLs. The ReSTOR group provided better uncorrected near visual acuity than the ReZoom group (P < 0.001), but similar to the Tecnis group. Spherical aberration was significantly higher in the ReZoom group (P = 0.007). Similar MTF curves were found for the aspheric multifocal IOL Tecnis and the spheric multifocal IOL ReSTOR, and both performed better than the multifocal IOL ReZoom in a 5 mm pupil (P < 0.001 at all spatial frequencies). Conclusions: Diffractive IOLs studied presented similar MTF curves for a 5 mm pupil diameter. Both diffractive IOLs showed similar spherical aberration, which was significantly better with the full-diffractive IOL Tecnis than with the refractive IOL ReZoom.

Optical Quality in Eyes Implanted With Aspheric and Spherical Intraocular Lenses Assessed by NIDEK OPD-Scan: A Randomized, Bilateral, Clinical Trial

PURPOSE: To determine whether implantation of an intraocular lens (IOL) with an aspheric surface (Akreos AO, Bausch & Lomb Inc) results in reduced ocular aberrations (spherical aberration) and improved Strehl ratio and modulation transfer function (MTF) after cataract surgery. METHODS: In an intraindividual, randomized, double-masked, prospective study of 50 eyes (25 patients) with bilateral cataract, an IOL with modified anterior and posterior surfaces (Akreos AO) was implanted in one eye and a biconvex IOL with spherical surfaces (Akreos Fit, Bausch & Lomb Inc) implanted in the fellow eye. Ocular aberrations, Strehl ratio, and MTF curve with 4.5-, 5.0-, and 6.0-mm pupils were measured with a NIDEK OPD-Scan dynamic retinoscopy aberrometer 3 months after surgery. Uncorrected and corrected distance visual acuity (UDVA and CDVA, respectively) were also measured. RESULTS: No statistically significant difference was noted between eyes in postoperative UDVA and CDVA at 1 month. At 3 months, the Akreos AO IOL group obtained statistically significant lower values of higher order and spherical aberrations with 4.5-, 5.0-, and 6.0-mm pupil diameters than the Akreos Fit IOL group (P<.05). The value of Strehl ratio was statistically significantly higher in eyes with the Akreos AO IOL for 4.5- and 6.0-mm pupils (P<.05). The MTF curve was better in the Akreos AO IOL group in 4.5-, 5.0-, and 6.0-mm pupils (P<.05). CONCLUSIONS: The aspheric Akreos AO IOL induced significantly less spherical aberration than the Akreos Fit IOL for 4.5-, 5.0-, and 6.0-mm pupils. Modulation transfer function and Strehl ratio were also better in eyes implanted with the Akreos AO IOL than the Akreos Fit. [J Refract Surg. 2011;27(4):287-292.] doi:10.3928/1081597X-20100714-01

Effects of bilateral adrenalectomy on systemic kainate-induced activation of the nucleus of the solitary tract. Regulation of blood pressure and local neurotransmitters

Glutamatergic transmission through metabotropic and ionotropic receptors, including kainate receptors, plays an important role in the nucleus of the solitary tract (NTS) functions. Glutamate system may interact with several other neurotransmitter systems which might also be influenced by steroid hormones. In the present study we analyzed the ability of systemic kainate to stimulate rat NTS neurons, which was evaluated by c-Fos as a marker of neuronal activation, and also to change the levels of NTS neurotransmitters such as GABA, NPY, CGRP, GAL, NT and NO by means of quantitative immunohistichemistry combined with image analysis. The analysis was also performed in adrenalectomized and kainate stimulated rats in order to evaluate a possible role of adrenal hormones on NTS neurotransmission. Male Wistar rats (3 month-old) were used in the present study. A group of 15 rats was submitted either to bilateral adrenalectomy or sham operation. Forty-eight hours after the surgeries, adrenalectomized rats received a single intraperitoneal injection of kainate (12 mg/kg) and the sham-operated rats were injected either with saline or kainate and sacrificed 8 hours later. The same experimental design was applied in a group of rats in order to register the arterial blood pressure. Systemic kainate decreased the basal values of mean arterial blood pressure (35%) and heart rate (22%) of sham-operated rats, reduction that were maintained in adrenalectomized rats. Kainate triggered a marked elevation of c-Fos positive neurons in the NTS which was 54% counteracted by adrenalectomy. The kainate activated NTS showed changes in the immunoreactive levels of GABA (143% of elevation) and NPY (36% of decrease), which were not modified by previous ablation of adrenal glands. Modulation in the levels of CGRP, GAL and NT immunoreactivities were only observed after kainate in the adrenalectomized rats. Treatments did not alter NOS labeling. It is possible that modulatory function among neurotransmitter systems in the NTS might be influenced by steroid hormones and the implications for central regulation of blood pressure or other visceral regulatory mechanisms control should be further investigated.

Bilateral lung transplantation in asymmetric thorax: Case reports

Suppurative lung diseases, such as cystic fibrosis and bronchiectasis, when diffuse and associated with important functional loss, can be treated with bilateral lung transplantation with good results. These diseases are frequently associated with previous lung resections presenting an asymmetric thorax, thus making lung extraction difficult and generating disproportion between the graft and the pleural cavity. To treat this condition, pneumonectomy and single lung transplantation is a feasible option; however, there are associated comorbidities and an invariable need for extracorporeal circulation. Described herein are 2 patients with an asymmetric thorax, treated with bilateral transplantation and lung volume reduction with lobectomy.