Study of the effect of M&A on real estate industry firms' performance

This paper proposes to adopt data envelopment analysis (DEA) based Malmquist total factor productivity (TFP) indices methods to evaluate the effect of mergers and acquisitions (M&As) on acquirers in short-term and long-term window. Based on analyzing 32 M&A deals conducted by Chinese real estate firms from 2000-2011, the study result demonstrate that the effect of M&A on developers’ performance is positive. Through M&A, the developers’ Malmquist TFP experienced a steady growth; their technology has got noticeable progress immediately after acquisition; and their technical efficiency has suffered a slight decrease in short-term after acquisition, but then achieved marked increase in the long-term when realization of integration and synergy. However, there is no evidence that the real estate firms have achieved scale efficiency improvement after M&A in either short-term or long-term.

Correlation between extent of osteolytic damage and metastatic burden of human breast cancer metastasis in nude mice : real-time PCR quantitation

Orthotopic or intracardiac injection of human breast cancer cell lines into immunocompromised mice allows study of the molecular basis of breast cancer metastasis. We have established a quantitative real-time PCR approach to analyze metastatic spread of human breast cancer cells inoculated into nude mice via these routes. We employed MDA-MB-231 human breast cancer cells genetically tagged with a bacterial β-galactosidase (Lac-Z) retroviral vector, enabling their detection by TaqMan® real-time PCR. PCR detection was linear, specific, more sensitive than conventional PCR, and could be used to directly quantitate metastatic burden in bone and soft organs. Attesting to the sensitivity and specificity of the PCR detection strategy, as few as several hundred metastatic MDA-MB-231 cells were detectable in 100 μm segments of paraffin-embedded lung tissue, and only in samples adjacent to sections that scored positive by histological detection. Moreover, the measured real-time PCR metastatic burden in the bone environment (mouse hind-limbs, n = 48) displayed a high correlation to the degree of osteolytic damage observed by high resolution X-ray analysis (r2 = 0.972). Such a direct linear relationship to tumor burden and bone damage substantiates the so-called 'vicious cycle' hypothesis in which metastatic tumor cells promote the release of factors from the bone which continue to stimulate the tumor cells. The technique provides a useful tool for molecular and cellular analysis of human breast cancer metastasis to bone and soft organs, can easily be extended to other cell/marker/organ systems, and should also find application in preclinical assessment of anti-metastatic modalities.

Multiplex real-time PCR for the detection and differentiation of equid herpesvirus 1 (EHV-1) and equid herpesvirus 4 (EHV-4).

A multiplex real-time PCR was designed to detect and differentiate equid herpesvirus 1 (EHV-1) and equid herpesvirus 4 (EHV-4). The PCR targets the glycoprotein B gene of EHV-1 and EHV-4. Primers and probes were specific to each equine herpesvirus type and can be used in monoplex or multiplex PCRs, allowing the differentiation of these two closely related members of the Alphaherpesvirinae. The two probes were minor-groove binding probes (MGB?) labelled with 6-carboxy-fluorescein (FAM?) and VIC® for detection of EHV-1 and EHV-4, respectively. Ten EHV-1 isolates, six EHV-1 positive clinical samples, one EHV-1 reference strain (EHV-1.438/77), three EHV-4 positive clinical samples, two EHV-4 isolates and one EHV-4 reference strain (EHV-4 405/76) were included in this study. EHV-1 isolates, clinical samples and the reference strain reacted in the EHV-1 real-time PCR but not in the EHV-4 real-time PCR and similarly EHV-4 clinical samples, isolates and the reference strain were positive in the EHV-4 real-time PCR but not in the EHV-1 real-time PCR. Other herpesviruses, such as EHV-2, EHV-3 and EHV-5 were all negative when tested using the multiplex real-time PCR. When bacterial pathogens and opportunistic pathogens were tested in the multiplex real-time PCR they did not react with either system. The multiplex PCR was shown to be sensitive and specific and is a useful tool for detection and differentiation of EHV-1 and EHV-4 in a single reaction. A comprehensive equine herpesvirus disease investigation procedure used in our laboratory is also outlined. This procedure describes the combination of alphaherpesvirus multiplex real-time PCR along with existing gel-based PCRs described by other authors.

The acceptability, usability and short-term outcomes of Get Real: A web-based program for psychotic-like experiences (PLEs)

Background Psychotic-like experiences (PLEs) are subclinical delusional ideas and perceptual disturbances that have been associated with a range of adverse mental health outcomes. This study reports a qualitative and quantitative analysis of the acceptability, usability and short term outcomes of Get Real, a web program for PLEs in young people. Methods Participants were twelve respondents to an online survey, who reported at least one PLE in the previous 3 months, and were currently distressed. Ratings of the program were collected after participants trialled it for a month. Individual semi-structured interviews then elicited qualitative feedback, which was analyzed using Consensual Qualitative Research (CQR) methodology. PLEs and distress were reassessed at 3 months post-baseline. Results User ratings supported the program's acceptability, usability and perceived utility. Significant reductions in the number, frequency and severity of PLE-related distress were found at 3 months follow-up. The CQR analysis identified four qualitative domains: initial and current understandings of PLEs, responses to the program, and context of its use. Initial understanding involved emotional reactions, avoidance or minimization, limited coping skills and non-psychotic attributions. After using the program, participants saw PLEs as normal and common, had greater self-awareness and understanding of stress, and reported increased capacity to cope and accept experiences. Positive responses to the program focused on its normalization of PLEs, usefulness of its strategies, self-monitoring of mood, and information putting PLEs into perspective. Some respondents wanted more specific and individualized information, thought the program would be more useful for other audiences, or doubted its effectiveness. The program was mostly used in low-stress situations. Conclusions The current study provided initial support for the acceptability, utility and positive short-term outcomes of Get Real. The program now requires efficacy testing in randomized controlled trials.

Abstract concepts made real: A pilot study examining pedagogical approaches in thermodynamics tutorials

BACKGROUND OR CONTEXT Thermodynamics is a core concept for mechanical engineers yet notoriously difficult. Evidence suggests students struggle to understand and apply the core fundamental concepts of thermodynamics with analysis indicating a problem with student learning/engagement. A contributing factor is that thermodynamics is a ‘science involving concepts based on experiments’ (Mayhew 1990) with subject matter that cannot be completely defined a priori. To succeed, students must engage in a deep-holistic approach while taking ownership of their learning. The difficulty in achieving this often manifests itself in students ‘not getting’ the principles and declaring thermodynamics ‘hard’. PURPOSE OR GOAL Traditionally, students practice and “learn” the application of thermodynamics in their tutorials, however these do not consider prior conceptions (Holman & Pilling 2004). As ‘hands on’ learning is the desired outcome of tutorials it is pertinent to study methods of improving their efficacy. Within the Australian context, the format of thermodynamics tutorials has remained relatively unchanged over the decades, relying anecdotally on a primarily didactic pedagogical approach. Such approaches are not conducive to deep learning (Ramsden 2003) with students often disengaged from the learning process. Evidence suggests (Haglund & Jeppsson 2012), however, that a deeper level and ownership of learning can be achieved using a more constructivist approach for example through self generated analogies. This pilot study aimed to collect data to support the hypothesis that the ‘difficulty’ of thermodynamics is associated with the pedagogical approach of tutorials rather than actual difficulty in subject content or deficiency in students. APPROACH Successful application of thermodynamic principles requires solid knowledge of the core concepts. Typically, tutorial sessions guide students in this application. However, a lack of deep and comprehensive understanding can lead to student confusion in the applications resulting in the learning of the ‘process’ of application without understanding ‘why’. The aim of this study was to gain empirical data on student learning of both concepts and application, within thermodynamic tutorials. The approach taken for data collection and analysis was: - 1 Four concurrent tutorial streams were timetabled to examine student engagement/learning in traditional ‘didactic’ (3 weeks) and non-traditional (3 weeks). In each week, two of the selected four sessions were traditional and two non-traditional. This provided a control group for each week. - 2 The non-traditional tutorials involved activities designed to promote student-centered deep learning. Specific pedagogies employed were: self-generated analogies, constructivist, peer-to-peer learning, inquiry based learning, ownership of learning and active learning. - 3 After a three-week period, teaching styles of the selected groups was switched, to allow each group to experience both approaches with the same tutor. This also acted to mimimise any influence of tutor personality / style on the data. - 4 At the conclusion of the trial participants completed a ‘5 minute essay’ on how they liked the sessions, a small questionnaire, modelled on the modified (Christo & Hoang, 2013)SPQ designed by Biggs (1987) and a small formative quiz to gauge the level of learning achieved. DISCUSSION Preliminary results indicate that overall students respond positively to in class demonstrations (inquiry based learning), and active learning activities. Within the active learning exercises, the current data suggests students preferred individual rather than group or peer-to-peer activities. Preliminary results from the open-ended questions such as “What did you like most/least about this tutorial” and “do you have other comments on how this tutorial could better facilitate your learning”, however, indicated polarising views on the nontraditional tutorial. Some student’s responded that they really like the format and emphasis on understanding the concepts, while others were very vocal that that ‘hated’ the style and just wanted the solutions to be presented by the tutor. RECOMMENDATIONS/IMPLICATIONS/CONCLUSION Preliminary results indicated a mixed, but overall positive response by students with more collaborative tutorials employing tasks promoting inquiry based, peer-to-peer, active, and ownership of learning activities. Preliminary results from student feedback supports evidence that students learn differently, and running tutorials focusing on only one pedagogical approached (typically didactic) may not be beneficial to all students. Further, preliminary data suggests that the learning / teaching style of both students and tutor are important to promoting deep learning in students. Data collection is still ongoing and scheduled for completion at the end of First Semester (Australian academic calendar). The final paper will examine in more detail the results and analysis of this project.

Measuring the effects of mergers and acquisitions on the economic performance of real estate developers

Real estate developers in China are using mergers and acquisitions (M&As) to ensure their survival and competitiveness. However, no suitable method is yet available to assess whether such M&As provide enhanced value for those involved. Using a hybrid method of data envelopment analysis (DEA) and Malmquist total factor productivity (TFP) indices, this paper evaluates the short and medium term effects of M&As on acquirers’ economic performance with a set of 32 M&A cases occurring during 2000–2011 in China. The results of the analysis show that M&As generally have a positive effect on acquirers’ economic performance. Acquisitions on average experienced a steady growth in developer Malmquist TFP, a more progressive adoption of technology immediately after acquisition, a slight short-term decrease in technical efficiency after acquisition but followed by a marked increase in the longer term once the integration and synergy benefits were realised. However, there is no evidence to show whether developers achieved any short or long term scale efficiency improvements after M&A. The findings of this study provide useful insights on developer M&A performance from an efficiency and productivity perspective.

Bovine cysticercosis-Development of a real-time PCR to enhance classification of suspect cysts identified at meat inspection

Laboratory confirmation methods are important in bovine cysticerosis diagnosis as other pathologies can result in morphologically similar lesions resulting in false identifications. We developed a probe-based real-time PCR assay to identify Taenia saginata in suspect cysts encountered at meat inspection and compared its use with the traditional method of identification, histology, as well as a published nested PCR. The assay simultaneously detects T. saginata DNA and a bovine internal control using the cytochrome c oxidase subunit 1 gene of each species and shows specificity against parasites causing lesions morphologically similar to those of T. saginata. The assay was sufficiently sensitive to detect 1 fg (Ct 35.09 +/- 0.95) of target DNA using serially-diluted plasmid DNA in reactions spiked with bovine DNA as well as in all viable and caseated positive control cysts. A loss in PCR sensitivity was observed with increasing cyst degeneration as seen in other molecular methods. In comparison to histology, the assay offered greater sensitivity and accuracy with 10/19 (53%) T. saginata positives detected by real-time PCR and none by histology. When the results were compared with the reference PCR, the assay was less sensitive but offered advantages of faster turnaround times and reduced contamination risk. Estimates of the assay's repeatability and reproducibility showed the assay is highly reliable with reliability coefficients greater than 0.94. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.

Real-time PCR as a surveillance tool for the detection of Trichinella infection in muscle samples from wildlife

Trichinella nematodes are the causative agent of trichinellosis, a meat-borne zoonosis acquired by consuming undercooked, infected meat. Although most human infections are sourced from the domestic environment, the majority of Trichinella parasites circulate in the natural environment in carnivorous and scavenging wildlife. Surveillance using reliable and accurate diagnostic tools to detect Trichinella parasites in wildlife hosts is necessary to evaluate the prevalence and risk of transmission from wildlife to humans. Real-time PCR assays have previously been developed for the detection of European Trichinella species in commercial pork and wild fox muscle samples. We have expanded on the use of real-time PCR in Trichinella detection by developing an improved extraction method and SYBR green assay that detects all known Trichinella species in muscle samples from a greater variety of wildlife. We simulated low-level Trichinella infections in wild pig, fox, saltwater crocodile, wild cat and a native Australian marsupial using Trichinella pseudospiralis or Trichinella papuae ethanol-fixed larvae. Trichinella-specific primers targeted a conserved region of the small subunit of the ribosomal RNA and were tested for specificity against host and other parasite genomic DNAs. The analytical sensitivity of the assay was at least 100 fg using pure genomic T. pseudospiralis DNA serially diluted in water. The diagnostic sensitivity of the assay was evaluated by spiking log of each host muscle with T. pseudospiralis or T. papuae larvae at representative infections of 1.0, 0.5 and 0.1 larvae per gram, and shown to detect larvae at the lowest infection rate. A field sample evaluation on naturally infected muscle samples of wild pigs and Tasmanian devils showed complete agreement with the EU reference artificial digestion method (k-value = 1.00). Positive amplification of mouse tissue experimentally infected with T. spiralis indicated the assay could also be used on encapsulated species in situ. This real-time PCR assay offers an alternative highly specific and sensitive diagnostic method for use in Trichinella wildlife surveillance and could be adapted to wildlife hosts of any region. (C) 2012 Elsevier B.V. All rights reserved.

An improved real-time PCR assay for the detection of Old World screwworm flies

The Old World screwworm (OWS) fly, Chrysomya bezziana, is a serious pest of livestock, wildlife and humans in tropical Africa, parts of the Middle East, the Indian subcontinent, south-east Asia and Papua New Guinea. Although to date Australia remains free of OWS flies, an incursion would have serious economic and animal welfare implications. For these reasons Australia has an OWS fly preparedness plan including OWS fly surveillance with fly traps. The recent development of an improved OWS fly trap and synthetic attractant and a specific and sensitive real-time PCR molecular assay for the detection of OWS flies in trap catches has improved Australia's OWS fly surveillance capabilities. Because all Australian trap samples gave negative results in the PCR assay, it was deemed necessary to include a positive control mechanism to ensure that fly DNA was being successfully extracted and amplified and to guard against false negative results. A new non-competitive internal amplification control (IAC) has been developed that can be used in conjunction with the OWS fly PCR assay in a multiplexed single-tube reaction. The multiplexed assay provides an indicator of the performance of DNA extraction and amplification without greatly increasing labour or reagent costs. The fly IAC targets a region of the ribosomal 16S mitochondrial DNA which is conserved across at least six genera of commonly trapped flies. Compared to the OWS fly assay alone, the multiplexed OWS fly and fly IAC assay displayed no loss in sensitivity or specificity for OWS fly detection. The multiplexed OWS fly and fly IAC assay provides greater confidence for trap catch samples returning negative OWS fly results. © 2014 International Atomic Energy Agency.

Studies on the international effects of real shocks

This doctoral thesis addresses the macroeconomic effects of real shocks in open economies in flexible exchange rate regimes. The first study of this thesis analyses the welfare effects of fiscal policy in a small open economy, where private and government consumption are substitutes in terms of private utility. The main findings are as follows: fiscal policy raises output, bringing it closer to its efficient level, but is not welfare-improving even though government spending directly affects private utility. The main reason for this is that the introduction of useful government spending implies a larger crowding-out effect on private consumption, when compared with the `pure waste' case. Utility decreases since one unit of government consumption yields less utility than one unit of private consumption. The second study of this thesis analyses the question of how the macroeconomic effects of fiscal policy in a small open economy depend on optimal intertemporal behaviour. The key result is that the effects of fiscal policy depend on the size of the elasticity of substitution between traded and nontraded goods. In particular, the sign of the current account response to fiscal policy depends on the interplay between the intertemporal elasticity of aggregate consumption and the elasticity of substitution between traded and nontraded goods. The third study analyses the consequences of productive government spending on the international transmission of fiscal policy. A standard result in the New Open Economy Macroeconomics literature is that a fiscal shock depreciates the exchange rate. I demonstrate that the response of the exchange rate depends on the productivity of government spending. If productivity is sufficiently high, a fiscal shock appreciates the exchange rate. It is also shown that the introduction of productive government spending increases both domestic and foreign welfare, when compared with the case where government spending is wasted. The fourth study analyses the question of how the international transmission of technology shocks depends on the specification of nominal rigidities. A growing body of empirical evidence suggests that a positive technology shock leads to a temporary decline in employment. In this study, I demonstrate that the open economy dimension can enhance the ability of sticky price models to account for the evidence. The reasoning is as follows. An improvement in technology appreciates the nominal exchange rate. Under producer-currency pricing, the exchange rate appreciation shifts global demand toward foreign goods away from domestic goods. This causes a temporary decline in domestic employment.

Real-Time PCR : A Molecular Approach to Investigate the Role of Intestinal Microbiota in the Pathophysiology of Irritable Bowel Syndrome

Irritable bowel syndrome (IBS) is a common multifactorial functional intestinal disorder, the pathogenesis of which is not completely understood. Increasing scientific evidence suggests that microbes are involved in the onset and maintenance of IBS symptoms. The microbiota of the human gastrointestinal (GI) tract constitutes a massive and complex ecosystem consisting mainly of obligate anaerobic microorganisms making the use of culture-based methods demanding and prone to misinterpretation. To overcome these drawbacks, an extensive panel of species- and group-specific assays for an accurate quantification of bacteria from fecal samples with real-time PCR was developed, optimized, and validated. As a result, the target bacteria were detectable at a minimum concentration range of approximately 10 000 bacterial genomes per gram of fecal sample, which corresponds to the sensitivity to detect 0.000001% subpopulations of the total fecal microbiota. The real-time PCR panel covering both commensal and pathogenic microorganisms was assessed to compare the intestinal microbiota of patients suffering from IBS with a healthy control group devoid of GI symptoms. Both the IBS and control groups showed considerable individual variation in gut microbiota composition. Sorting of the IBS patients according to the symptom subtypes (diarrhea, constipation, and alternating predominant type) revealed that lower amounts of Lactobacillus spp. were present in the samples of diarrhea predominant IBS patients, whereas constipation predominant IBS patients carried increased amounts of Veillonella spp. In the screening of intestinal pathogens, 17% of IBS samples tested positive for Staphylococcus aureus, whereas no positive cases were discovered among healthy controls. Furthermore, the methodology was applied to monitor the effects of a multispecies probiotic supplementation on GI microbiota of IBS sufferers. In the placebo-controlled double-blind probiotic intervention trial of IBS patients, each supplemented probiotic strain was detected in fecal samples. Intestinal microbiota remained stable during the trial, except for Bifidobacterium spp., which increased in the placebo group and decreased in the probiotic group. The combination of assays developed and applied in this thesis has an overall coverage of 300-400 known bacterial species, along with the number of yet unknown phylotypes. Hence, it provides good means for studying the intestinal microbiota, irrespective of the intestinal condition and health status. In particular, it allows screening and identification of microbes putatively associated with IBS. The alterations in the gut microbiota discovered here support the hypothesis that microbes are likely to contribute to the pathophysiology of IBS. The central question is whether the microbiota changes described represent the cause for, rather than the effect of, disturbed gut physiology. Therefore, more studies are needed to determine the role and importance of individual microbial species or groups in IBS. In addition, it is essential that the microbial alterations observed in this study will be confirmed using a larger set of IBS samples of different subtypes, preferably from various geographical locations.

Learning from positive and unlabelled examples using maximum margin clustering

Learning from Positive and Unlabelled examples (LPU) has emerged as an important problem in data mining and information retrieval applications. Existing techniques are not ideally suited for real world scenarios where the datasets are linearly inseparable, as they either build linear classifiers or the non-linear classifiers fail to achieve the desired performance. In this work, we propose to extend maximum margin clustering ideas and present an iterative procedure to design a non-linear classifier for LPU. In particular, we build a least squares support vector classifier, suitable for handling this problem due to symmetry of its loss function. Further, we present techniques for appropriately initializing the labels of unlabelled examples and for enforcing the ratio of positive to negative examples while obtaining these labels. Experiments on real-world datasets demonstrate that the non-linear classifier designed using the proposed approach gives significantly better generalization performance than the existing relevant approaches for LPU.

A facultatividade da concordância: português formal real versus gramática escolar

No ensino de língua nacional, concordância é um dos tópicos em cujo aprendizado observa dificuldade por parte dos discentes, principalmente pelo grande número de regras facultativas das gramáticas, que muitas vezes não levam em conta o uso formal real da língua. Este trabalho visa a descrever esse uso, a partir da observação de um corpus do caderno opinião de jornais de grande circulação, confrontando os resultados com as prescrições da norma gramatical escolar, a fim de separar, em tais prescrições, a parte aproveitável da não coincidente com a realidade do corpus, se for o caso. Pretende-se, dessa forma, contribuir para a boa qualidade do ensino da língua portuguesa nos níveis fundamental e médio, especificamente no que se refere à concordância

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

Matrices whose hermitian part is positive definite

We are concerned with the class ∏_n of nxn complex matrices A for which the Hermitian part H(A) = A+A*/2 is positive definite.

Various connections are established with other classes such as the stable, D-stable and dominant diagonal matrices. For instance it is proved that if there exist positive diagonal matrices D, E such that DAE is either row dominant or column dominant and has positive diagonal entries, then there is a positive diagonal F such that FA ϵ ∏_n.

Powers are investigated and it is found that the only matrices A for which A^m ϵ ∏_n for all integers m are the Hermitian elements of ∏_n. Products and sums are considered and criteria are developed for AB to be in ∏_n.

Since ∏_n n is closed under inversion, relations between H(A)^-1 and H(A^-1) are studied and a dichotomy observed between the real and complex cases. In the real case more can be said and the initial result is that for A ϵ ∏_n, the difference H(adjA) - adjH(A) ≥ 0 always and is ˃ 0 if and only if S(A) = A-A*/2 has more than one pair of conjugate non-zero characteristic roots. This is refined to characterize real c for which cH(A^-1) - H(A)^-1 is positive definite.

The cramped (characteristic roots on an arc of less than 180°) unitary matrices are linked to ∏_n and characterized in several ways via products of the form A ^-1A*.

Classical inequalities for Hermitian positive definite matrices are studied in ∏_n and for Hadamard's inequality two types of generalizations are given. In the first a large subclass of ∏_n in which the precise statement of Hadamardis inequality holds is isolated while in another large subclass its reverse is shown to hold. In the second Hadamard's inequality is weakened in such a way that it holds throughout ∏_n. Both approaches contain the original Hadamard inequality as a special case.