Search

Economical dispatch plays an important role in the operation of DC micro-grid. This paper presents a modified $\lambda$ -consensus method that can achieve the optimal economical dispatch subjected to voltage regulation constraints. Simulation results verify the feasibility of the proposed scheme.

Energy storage systems (ESSs) could help maintain real-time power balance of islanded microgrids, but they cost too much. In this paper we propose a coordinated control strategy without communication for an islanded microgrid, where less ESSs are installed. The microgrid is made up of photovoltaics (PVs) and ESSs inverters and loads. In the proposed method, PVs can achieve both MPPT operation and frequency regulation by using adaptive frequency droop. In the meanwhile, PVs can curtail the output power and switch to proportional droop to support the microgrid when ESSs are insufficient to absorb the surplus power. For ESSs, the droop control is adopted for grid-supporting ability until the limit of charging power is activated by the power limit controller. Generally, the control strategy for each unit is able to softly and autonomously switch to the proper mode based on the state of charge (SOC) of ESSs, the total load demand and the frequency level in the microgrid. Besides, the control strategy can coordinate the AC microgrid with arbitrary PVs and ESSs. Furthermore, the small-signal models of the microgrid in different modes are established to analyze the design of control coefficients. Finally, the proposed strategy is validated in Matlab/Simulink simulation and hardware-in-loop (HIL) tests under different cases.

Power oscillation is observed when a disturbance occurs in multiple virtual synchronous generators (VSGs) grid, potentially impacting the safe operation of the systems. This article proposes a distributed adaptive virtual inertia control method for suppressing the power oscillation and improving dynamic frequency response in the multiple VSGs grid. The basic principle of the method is that when the local frequency of a VSG deviates from the average frequency of its neighbors, the adaptive inertia control will exhibit a large inertia and when the local frequency starts to return, a small inertia is shaped to accelerate the convergence to the average frequency. The stability of the proposed algorithm is proved by the Lyapunov stability theory, and the guidelines on the key control parameters are provided. Finally, the simulation results and hardware-in-loop results demonstrate the effectiveness of the proposed control method.

In this paper, we survey some recent results on the existence of bounded plurisubharmonic functions on pseudoconvex domains, the Diederich–Fornaess exponent and its relations with existence of domains with Levi-flat boundary in complex manifolds.

Nevoid basal cell carcinoma syndrome (NBCCS) is a rare autosomal dominant disease characterized by the development of multiple jaw keratocysts and basal cell carcinomas (BCC) and accompanied by diverse phenotypes. The establishment of diagnosis lies on the identification of a heterozygous germline pathogenic variant in the patched homolog 1 gene (PTCH1). PTCH1 has alternative splicing and selective initial coding exon, leading to three types of encoding proteins (PTCHL, PTCHM and PTCHS). The expression of each protein in NBCCS remains ambiguous, especially the importance of the first two exons in translation. Here, we report a Chinese NBCCS family of a novel PTCH1 heterozygous mutation (IVS 2, c.394+1G>T, g.10652G>T) identified by genomic sequencing and reverse-transcription-PCR as aberrant splicing. To the best of our knowledge, this is the first report of NBCCS with a splicing site mutation in intron 2 resulting in exon 2 skipping. Our finding suggests that exon 2 plays an important role in the development of NBCCS and further speculates that the role of longer isoforms PTCHL and PTCHM is crucial in NBCCS, while that of short isoform PTCHS might be dispensable.

// Siqi Fu 1, * , Haijing Wu 1, * , Huiming Zhang 1 , Christine G. Lian 2 and Qianjin Lu 1 1 Department of Dermatology, Second Xiangya Hospital, Central South University, Hunan Key Laboratory of Medical Epigenomics, Changsha, Hunan, China 2 Program in Dermatopathology, Department of Pathology, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA * These authors have contributed equally to this work Correspondence to: Lu Qianjin, email: qianlu5860@gmail.com Keywords: melanoma, 5-hmC, 5-mC, epigenetic therapy, TET Received: March 02, 2017 Accepted: May 03, 2017 Published: May 30, 2017 ABSTRACT Melanoma is a malignant tumor of melanocytes and is considered to be the most aggressive cancer among all skin diseases. The pathogenesis of melanoma has not been well documented, which may restrict the research and development of biomarkers and therapies. To date, several genetic and epigenetic factors have been identified as contributing to the development and progression of melanoma. Besides the findings on genetic susceptibilities, the recent progress in epigenetic studies has revealed that loss of the DNA hydroxymethylation mark, 5-hydroxymethylcytosine (5-hmC), along with high levels of DNA methylation at promoter regions of several tumor suppressor genes in melanoma, may serve as biomarkers for melanoma. Moreover, 5-Aza-2′-deoxycytidine, an epigenetic modifier causing DNA demethylation, and ten-eleven translocation family dioxygenase (TET), which catalyzes the generation of 5-hmC, demonstrate therapeutic potential in melanoma treatment. In this review, we will summarize the latest progress in research on DNA methylation/hydroxymethylation in melanoma, and we will discuss and provide insight for epigenetic biomarkers and therapies for melanoma. Particularly, we will discuss the role of DNA hydroxymethylation in melanoma infiltrating immune cells, which may also serve as a potential target for melanoma treatment.

// Heng Yin 1 , Haijing Wu 1 , Ming Zhao 1 , Qing Zhang 1 , Hai Long 1 , Siqi Fu 1 and Qianjin Lu 1 1 Department of Dermatology, Second Xiangya Hospital, Central South University, Hunan Key Laboratory of Medical Epigenomics, Changsha, Hunan, China Correspondence to: Qianjin Lu, email: qianlu5860@gmail.com Keywords: JMJD3, H3K27me3, CD11a, SLE, CD4 + T cells Received: February 13, 2017 Accepted: March 28, 2017 Published: April 06, 2017 ABSTRACT Aberrant CD11a overexpression in CD4 + T cells induces T cell auto-reactivity, which is an important factor for systemic lupus erythematosus (SLE) pathogenesis. Although many studies have focused on CD11a epigenetic regulation, little is known about histone methylation. JMJD3, as a histone demethylase, is capable of specifically removing the trimethyl group from the H3K27 lysine residue, triggering target gene activation. Here, we examined the expression and function of JMJD3 in CD4 + T cells from SLE patients. Significantly decreased H3K27me3 levels and increased JMJD3 binding were detected within the ITGAL (CD11a) promoter locus in SLE CD4 + T cells compared with those in healthy CD4 + T cells. Moreover, overexpressing JMJD3 through the transfection of pcDNA3.1-JMJD3 into healthy donor CD4 + T cells increased JMJD3 enrichment and decreased H3K27me3 enrichment within the ITGAL (CD11a) promoter and up-regulated CD11a expression, leading to T and B cell hyperactivity. Inhibition of JMJD3 via JMJD3-siRNA in SLE CD4 + T cells showed the opposite effects. These results demonstrated that histone demethylase JMJD3 regulates CD11a expression in lupus T cells by affecting the H3K27me3 levels in the ITGAL (CD11a) promoter region, and JMJD3 might thereby serve as a potential therapeutic target for SLE.

Let \(\Omega ={\widetilde{\Omega }}{\setminus } \overline{D}\) where \({\widetilde{\Omega }}\) is a bounded domain with connected complement in \({\mathbb {C}}^n\) (or more generally in a Stein manifold) and D is relatively compact open subset of \({\widetilde{\Omega }}\) with connected complement in \(\widetilde{\Omega }\). We obtain characterizations of pseudoconvexity of \({\widetilde{\Omega }}\) and D through the vanishing or Hausdorff property of the Dolbeault cohomology groups of \(\Omega \) on various function spaces. In particular, we show that if the boundaries of \({\widetilde{\Omega }}\) and D are Lipschitz and \(C^2\)-smooth respectively, then both \({\widetilde{\Omega }}\) and D are pseudoconvex if and only if 0 is not in the spectrum of the \(\overline{\partial }\)-Neumann Laplacian of \(\Omega \) on (0, q)-forms for \(1\le q\le n-2\) when \(n\ge 3\); or 0 is not a limit point of the spectrum of the \(\overline{\partial }\)-Neumann Laplacian on (0, 1)-forms when \(n=2\).

Background:. Plastic surgeons desire more efficient methods of processing lipoaspirate when performing fat grafting procedures. We compared, in a preclinical study, the quantity and quality of lipoaspirate processed by a novel Poloxamer Wash, Absorption, mesh filtration System (PWAS) to a frequently used Ringer’s Lactate wash, Decant, and mesh filtration System (RLDS). Methods:. Lipoaspirate from 10 patients was processed with the RLDS and PWAS systems. The processed lipoaspirate from each device was centrifuged to quantify the amount of fat, free oil, and aqueous components remaining in the fat graft. A trypan blue dye exclusion test assessed cell viability. The processing time for the lipoaspirate was also measured. Results:. The 10-patient average fat volume processed and available for grafting was similar using both systems. The adipose volume fraction of PWAS was greater (89% ± 3%) than RLDS (76% ± 10%, P = 0.02). The trypan blue exclusion values and processing time were similar for both systems. Oil was efficiently removed from the lipoaspirate, and both systems processed fat efficiently. Conclusion:. The PWAS effectively cleans lipoaspirate with increased fat concentration.

Most studies about the developing representation of numerical information and non-numerical ordered sequences involved Western children. It is not as certain that children from other parts of the world display a similar pattern. Moreover, the issue of gender differences was seldom considered. To shed more light on the above issues, we conducted four experiments involving a total of 322 1st and 2nd graders in Mainland China. Children either estimated the locations of numbers on number lines or the locations of months on month lines. Across four experiments, children produced estimates consistent with a linear function for smaller numbers. For larger numbers and months, younger children produced estimates consistent with a logarithmic function but older children's estimates were best fitted through a linear function. There were complex differences between boys and girls: Overall, whereas boys were more accurate estimating numbers, girls were better at estimating months. In conclusion, the representation of numerical order in Chinese numbers mirrored the representation of numerical order in Arabic numbers, demonstrating the universal developmental pattern of numerical representation from the less accurate logarithmic function to the more accurate linear function. Also, like Western children, Chinese children's representation of non-numerical order showed the same developmental pattern as numerical order, although this ability appeared to be first acquired in the numerical domain.

Background Wilms’ tumor 1-associating protein (WTAP) is a ubiquitously expressed nuclear protein, and involved in multiple pathophysiological processes, including cell cycle, RNA splicing and stabilization, N6-methyladenosine RNA modification, cell proliferation, and apoptosis as well as embryonic development. Here, we investigated the specific role of WTAP in the pathogenesis of psoriasis and its underlying mechanism. Methods Reverse transcription-quantitative polymerase chain reaction (RT-qPCR), western blot analyses and multi-spectrum immunohistochemistry were applied to evaluate the level of WTAP expression in psoriatic skin and normal skin. HaCaT cells was stably transfected with WTAP small interfering (si)RNA and plasmid using Lipofectamine®2000 and proliferation was determined by CCK8. Apoptosis and cell cycle analysis were conducted by flow cytometry. Western blot assay was used to explore the expression levels of cell cycle-related proteins in HaCaT cells after WTAP overexpression or inhibition. Furthermore, HaCaT cells were stimulated with proinflammatory cytokines (ie, IL-17A, IL-22, IL-1a, oncostatin M, and TNF-a) to assess WTAP expression. Results We demonstrated that the mRNA and protein levels of WTAP were significantly increased in lesional skins of psoriasis patients and psoriatic cell model compared with normal controls. WTAP was highly expressed in epidermis rather than dermis. Overexpression of WTAP promoted keratinocytes proliferation, which might be related to the up-regulation of cyclinA2 and CDK2. Conclusions These results indicate that overexpression of WTAP may contribute to the pathogenesis of psoriasis by regulating cell cycle progression and highlight WTAP as a potential therapeutic target for psoriasis treatment.

Dermatomyofibroma is a benign and rare proliferation of myofibroblasts and fibroblasts of the skin. Dermatomyofibroma commonly locates at the shoulder and neck of young adults and adolescents. Other frequently affected anatomic sites are upper arms, thigh, chest wall, back, axillary region and abdomen. Herein, we reported a case of dermatomyofibroma occurred in the nasion. The asymptomatic firm nodule and histopathological features were consistent with dermatomyofibroma. Immunohistochemically, the tumor cells expressed vimentin, HHF35 and α-smooth muscle actin (α-SMA). The patient was followed up for 2 years after excision of the tumors and recurrences were not observed.皮肤肌纤维瘤是一种少见的良性皮肤软组织肿瘤，病变为成纤维细胞和肌成纤维细胞增殖，常见于年轻成年人和青少年的肩部及颈部，其次好发于上臂、大腿、胸壁、背部、腋窝和腹部。本文报道1例罕见发生于鼻部的皮肤肌纤维瘤，此例肿物表现为无症状的坚硬的皮肤结节，病理上证实与皮肤肌纤维瘤相符。免疫组织化学结果显示，肿瘤细胞表达波形蛋白(vimentin)、肌特异性肌动蛋白(HHF35)和平滑肌肌动蛋白(α-smooth muscle actin，α-SMA)。手术切除后随访2年无复发。.

We study the Diederich–Fornaess exponent and relate it to non-existence of Stein domains with Levi-flat boundaries in complex manifolds. In particular, we prove that if the Diederich–Fornaess exponent of a smooth bounded Stein domain in an $$n$$ -dimensional complex manifold is greater than $$k/n$$ , then it has a boundary point at which the Levi-form has rank greater than or equal to k.

Background Both in vivo and in vitro, cells are subjected to mechanical stress, which can affect their proliferation and differentiation. However, the detailed mechanisms of the accompanying morphologic and biochemical changes remain elusive. This is partially caused by the lack of suitable stretch model and method that mimic soft tissue expansion used in plastic surgery. In this study, we report the development of a novel model for uniaxial stretch cell mimicking tissue expansion. Materials and methods Fibroblasts, grown in plastic culture caskets, were stretched in a progressive and accumulative manner lasting from 1 to 4 days. Cell proliferation was measured using the methyl thiazolyl tetrazolium assay and the Western blot analysis of cell cycle proteins. Results Following the stretch protocol, fibroblasts elongated and aligned parallel to each other and to the applied strain vectors. Furthermore, stretch-stimulated cell proliferation was compared with the unstretched conditions. Conclusions These results demonstrate that this uniaxial cell stretcher device and the accumulative stretch method are a suitable system for mimicking the tissue expansion process used in clinical applications. Level of evidence Not gradable.

Cicatricial ectropion of the upper eyelid is a serious problem because of the association with exposure keratitis and ulceration. Traditional surgical treatment usually requires skin grafts or local flaps depending on the severity of the defect. However, outcomes have usually been discouraging, especially in terms of cosmetic appearance.From February 2000 to March 2012, a total of 12 upper eyelids with severe cicatricial ectropion were treated with a retrograde postauricular island flap and were included in this study. Based on the pedicle of the parietal branch of the superficial temporal artery and its choke anastomoses to the posterior auricular artery, the retrograde postauricular island flap was harvested with a supra-auricular incision down to the non-hair-bearing side skin of the postauricular region. The flap was then transferred to the upper-lid lesion by passing it through a subcutaneous tunnel between the pedicle base and the upper-lid lesion. The donor site was directly closed by advancing the postauricular scalp flap into the sulcus. The largest flap was 6.5 × 3.5 cm(2).After 6-12 months of follow-up, flaps survived with good color, texture, and contour. The eyelids moved freely without recurrence of ectropion. The donor site had an inconspicuous scar. No major complications occurred.The retrograde postauricular island flap can be a safe, simple, and effective procedure for aesthetic correction of severe cicatricial upper-eyelid ectropion with few complications and little donor-site morbidity.This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

We obtain several results about stability of the Bergman kernel on a tower of coverings on complex manifolds. An effective version of Rhodes' result is given for a tower of coverings on a compact Riemann surface of genus greater than or equal to 2. Stability of the Bergman kernel is established for towers of coverings on hyperbolic Riemann surfaces and on complete Kaehler manifolds satisfying certain potential conditions. As a consequence, stability of the Bergman kernel is established for any tower of coverings of Riemann surfaces when the top manifold is simply-connected., Comment: 22 pages

The quotient of the Szego and Bergman kernels for a smooth bounded pseudoconvex domains in C n is bounded from above by a constant multiple of δ | log δ | p for any p > n , where δ is the distance to the boundary. For a class of domains that includes those of DʼAngelo finite type and those with plurisubharmonic defining functions, the quotient is also bounded from below by a constant multiple of δ | log δ | p for any p − 1 . Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.

Estimates of the Kobayashi metric in the normal direction are used to study the mapping problem in several complex variables., Comment: 13 pages; to appear in the special issue of Complex Variables and Elliptic Equations on holomorphic mappings edited by Steven Krantz and John Erik Fornaess

A smooth bounded pseudoconvex domain in C2 is of finite type if and only if the number of eigenvalues of its a-Neumann Laplacian that are less than or equal to ? has at most polynomial growth as ? goes to infinity.

The spectrum of the ∂-Neumann Laplacian on a polydisc in C" is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, some of which, in particular the smallest ones, are of infinite multiplicity.

Compactness of the Neumann operator in the ∂ ¯ -Neumann problem is studied for weakly pseudoconvex bounded Hartogs domains in two dimensions. A nonsmooth domain is constructed for which condition (P) fails to hold, yet the Kohn Laplacian still has compact resolvent. The main result, in contrast, is that for smoothly bounded Hartogs domains, the well-known sufficient condition (P) is equivalent to compactness. The analyses of compactness and condition (P) boil down to the asymptotic behavior of the lowest eigenvalues of two related sequences of Schrodinger operators, one with a magnetic field and one without, parametrized by a Fourier variable resulting from the Hartogs symmetry. The nonsmooth example is based on the Aharonov–Bohm phenomenon of quantum physics. For smooth domains not satisfying (P), we prove that there always exists an exceptional sequence of Fourier variables for which the Aharonov–Bohm effect is weak and thence that compactness fails to hold. This sequence can be very sparse, so that the lack of compactness is due to a rather subtle effect.

Formulas that relate the Bergman kernel and projection of a bounded Reinhardt domain whose closure does not intersect the coordinate planes to those of its covering tube domain are obtained via the Poisson summation formula.

In this paper, we study the problem of classification of piecewise smooth domains in with non-compact automorphism groups. We prove that a simply-connected domain in with generic piecewise smooth Levi-flat boundary and non-compact automorphism group is biholomorphic to a bidisc.

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in C 3 \mathbb {C}^3 defined by the inequality | z 1 | + | z 2 | + | z 3 | > 1 |z_1|+|z_2|+|z_3|>1 , have zeroes.

To find new ways for wound healing and tissue expansion by reviewing of progress in recent years in functional molecules which are used for signaling channels of mechanical stress perception and mechanotransduction of keratinocyte.The domestic and international articles were reviewed to summarize the functional molecules and signaling channels of mechanical stress perception and mechanotransduction of keratinocytes.The mechanism of mechanical stress perception includes mechano-sensitive channels, growth factor receptor-mediated mechanical stress perception, and mechanical stress perception by protein deformation. The mechanism of mechanotransduction includes cell adhesion-mediated signaling, mitogen-activated protein kinase signaling, the cytoskeleton and extracellular matrix, and so on.Keratinocytes can response to the mechanical stress and transfer the effective information to undergo shaping, migration, proliferation, differentiation, and other biological behavior in order to adjust itself to adapt to the new environment.

Summary Background The expanded forehead flap, using temporal pedicles, has been employed extensively in facial reconstruction. To overcome the disadvantages of the traditional dual temporal pedicles, such as the limited transfer range and the short length of the flap, the distal supercharging technique can be applied to lengthen the flap and extend the transfer range, especially in the cases with a past temporal burn injury. This article aims to present an application of the distal supercharged expanded forehead flap procedure for hemi-facial reconstruction and discuss the haemodynamics of the expanded forehead flap. Methods The tissue expander implantation and the following forehead tissue expansion were performed regularly. When the forehead skin expansion was completed, an expanded forehead flap was created and transferred to the damaged facial area with one distal temporal vessel pedicle that was anastomosed with facial vessels in a supercharged way. All patients were analysed retrospectively. Results From September 2009 to September 2011, eight male patients and one female patient were treated using this method. Their flaps size ranged from 20 cm × 8 cm to 30 cm × 11 cm and no flap loss occurred. Patients came in for follow-ups 9–16 months after the procedures. All the patients were satisfied with the results. Conclusions The supercharging expanded forehead flap procedure can provide reliable flap vascularity due to its elastic transferring abilities. By using a distal supercharging technique, we can lengthen and widen the flap to tailor it to the defect, while also minimising the donor defect in the patients with a past temporal injury.

Cleft palate is one of the most common congenital malformations in the maxillofacial region. After a cleft palate repair, surgeons must deal with the transverse growth restriction and palatal fistulas caused by scar tissue on the raw bone surface around the hard palate. This report describes the technique of the buccinator musculomucosal flap procedure performed together with repair of the cleft palate. The objective is to cover exposed bone areas of the hard palate to decrease scar contraction and subsequent transverse maxillary growth restriction, as well as tension at the closure.From August 2009 to February 2012, 15 patients underwent the buccinator musculomucosal flap procedure. First, the cleft palate was repaired by mucoperiosteal flaps, resulting in wide and raw bone surfaces around the hard palate. The outline of the flap was marked on the buccal mucosa. Grounding on the exposed bone areas around the hard palate, the authors designed widths of flaps ranging from 1.5 to 2.5 cm. These flaps were elevated from the buccopharyngeal fascia and turned 90° to cover the raw hard palate bone surfaces. The donor sites were closed by direct suture.The follow-up period was 1-26 months (average, 10 months). No complications were found in any patient who underwent the procedure, and no fistulas occurred in the midline of the palate. No patients experienced complications related to the donor sites. No trismus or other dysfunction related to mouth movement was observed.The buccinator musculomucosal flap is a convenient and safe flap procedure with fewer donor-site complications. This procedure also has significant potential for improving maxilla growth and reducing the secondary complications that often can result from cleft palate repair.This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

We prove that, if ρ is a boundary point of a smoothly bounded pseudoconvex Reinhardt domain in , then the variety type at ρ is identical to the regular type.

The asymptotic behavior of the holomorphic sectional curvature of the Bergman metric on a pseudoconvex Reinhardt domain of finite type in ℂ2 is obtained by rescaling locally the domain to a model domain that is either a Thullen domain Ω m = {(z 1,z 2); ¦z 1¦2 + ¦z 2¦2m < 1 or a tube domainT m = {(z 1,z 2); Imz1 + (Imz2)2m < 1}. The Bergman metric for the tube domainT m is explicitly calculated by using Fourier-Laplace transformation. It turns out that the holomorphic sectional curvature of the Bergman metric on the tube domainT m at (0, 0) is bounded above by a negative constant. These results are used to construct a complete Kahler metric with holomorphic sectional curvature bounded above by a negative constant for a pseudoconvex Reinhardt domain of finite type in ℂ2.

In this paper we obtain the asymptotic expansions of the Carathéodory and Kobayashi metrics of strictly pseudoconvex domains with C∞ smooth boundaries in ℂn. The main result of this paper can be stated as following:Main Theorem. Let Ω be a strictly pseudoconvex domain with C∞ smooth boundary. Let FΩ(z,X) be either the Carathéodory or the Kobayashi metric of Ω. Let δ(z) be the signed distance from z to ∂Ω with δ(z) < 0 for z ∊ Ω and δ(z) ≥ 0 for z ∉ Ω. Then there exist a neighborhood U of ∂Ω, a constant C > 0, and a continuous function C(z,X):(U ∩ Ω) × ℂn -> ℝ such that and|C(z,X)| ≤ C|X| for z ∊ U ∩ Ω and X ∊ ℂn

Acne inverse (AI), also known as hidradenitis suppurativa, is characterized by inflammatory nodules, fistulating sinus tracts, and painful skin abscesses. The severe AI often produces disfiguring scars influenced in both the appearance and function, especially in the facial and cervical regions. There might be difficulties in the situation for surgical treatment. This report described a 26-year-old man with severe scarring contractures in the neck and mandible regions after a long-term AI treated successfully with a bilateral pedicled expanded forehead flap. With the achievement of mental cervical angle, the patient has been reconstructed well both aesthetically and functionally during the long-term follow-ups.

We discuss and expand upon our previous results on comparison of the Bergman and the Szego kernels. We also study the relations between the Bergman growth exponent and the finite type conditions.

We study the \( \bar \partial \)-Neumann Laplacian from spectral theoretic perspectives. In particular, we show how pseudoconvexity of a bounded domain is characterized by positivity of the \( \bar \partial \)-Neumann Laplacian.

A bounded domain in several complex variables with connected Lipschitz boundary is pseudoconvex if and only if the bottom of the (essential) spectrum of the Kohn Laplacian is positive on all (0, q)-forms with square-integrable coefficients., 8 pages

In this paper we study the concepts of spectral domain and complete spectral domain in several complex variables. For a domain Ω in Cn and an n-tuple T of commuting operators on a Hilbert space H such that the Taylor spectrum of T is a subset of Ω, we introduce the quantities KΩ(T ) and MΩ(T ). These quantities are related to the quantities KX(T ) and MX(T ) introduced by Paulsen for a compact subset X. When T is an n-tuple of 2×2 matrices, KΩ(T ) and MΩ(T ) are expressed in terms of the Caratheodory metric and the Mobius distance. This in turn answers a question by Paulsen for tuples of 2×2 matrices. We also establish von Neumann’s inequality for an n-tuple of upper triangular Toeplitz matrices. We study the regularity of KΩ(T ) and MΩ(T ) and obtain various comparisons of these two quantities when T is an n-tuple of Jordan blocks.

We give, in dimensions three or greater, an example of a bounded, pseudoconvex, circular domain in complex space with smooth real analytic boundary and non-compact automorphism group which is not biholomorphically equivalent to any Reinhardt domain. We give an analogous example in dimension two, but the domain fails to be smooth at one boundary point---indeed it is not in any Lipschitz class at the exceptional point.

We give an explicit description of smoothly bounded Reinhardt domains with noncompact automorphism groups. In particular, this description confirms a special case of a conjecture of Greene/Krantz.

In this note we obtain a sharp estimate of the Bergman kernels near C 2 {\mathcal {C}^2} boundary points of pseudoconvex domains by induction on the dimension and a theorem of Ohsawa-Takegoshi.

We study the classification of smoothly bounded domains in complex manifolds that cover compact sets. We prove that a smoothly bounded domain in a hyperbolic complex surface that covers a compact set is either biholomorphic to the ball or covered by the bidisc.