Application of Haar functions for transmission line and transformer differential protection

The development of algorithms, based on Haar functions, for extracting the desired frequency components from transient power-system relaying signals is presented. The applications of these algorithms to impedance detection in transmission line protection and to harmonic restraint in transformer differential protection are discussed. For transmission line protection, three modes of application of the Haar algorithms are described: a full-cycle window algorithm, an approximate full-cycle window algorithm, and a half-cycle window algorithm. For power transformer differential protection, the combined second and fifth harmonic magnitude of the differential current is compared with that of fundamental to arrive at a trip decision. The proposed line protection algorithms are evaluated, under different fault conditions, using realistic relaying signals obtained from transient analysis conducted on a model 400 kV, 3-phase system. The transformer differential protection algorithms are also evaluated using a variety of simulated inrush and internal fault signals.

Androgen receptor-dependent and independent functions of ARIP4

Androgen receptor (AR) is necessary for normal male phenotype development and essential for spermatogenesis. AR is a classical steroid receptor mediating actions of male sex steroids testosterone and 5-alpha-dihydrotestosterone. Numerous coregulators interact with the receptor and regulate AR activity on target genes. This study deals with the characterization of androgen receptor-interacting protein 4 (ARIP4). ARIP4 binds DNA, interacts with AR in vitro and in cultured yeast and mammalian cells, and modulates AR-dependent transactivation. ARIP4 is an active DNA-dependent ATPase, and this enzymatic activity is essential for the ability of ARIP4 to modulate AR function. On the basis of sequence homology in its ATPase domain, ARIP4 belongs to the SNF2 family of proteins involved in chromatin remodeling, DNA repair, and homologous recombination. Similar to its closest homologs ATRX and Rad54, ARIP4 does not seem to be a classical chromatin remodeling protein in that it does not appear to form large protein complexes in vivo or remodel mononucleosomes in vitro. However, ARIP4 is able to generate superhelical torsion on linear DNA fragments. ARIP4 is covalently modified by SUMO-1, and mutation of six potential SUMO attachment sites abolishes the ability of ARIP4 to bind DNA, hydrolyze ATP, and activate AR function. ARIP4 expression starts in early embryonic development. In mouse embryo ARIP4 is present mainly in the neural tube and limb buds. In adult mouse tissues ARIP4 expression is virtually ubiquitous. In mouse testis ARIP4 is expressed in the nuclei of Sertoli cells in a stage-dependent manner. ARIP4 is also present in the nuclei of Leydig cells, spermatogonia, pachytene and diplotene spermatocytes. Testicular expression pattern of ARIP4 does not differ significantly in wild-type, FSHRKO, and LuRKO mice. In the testis of hpg mice, ARIP4 is found mainly in interstitial cells and has very low, if any, expression in Sertoli and germ cells. Heterozygous Arip4+/ mice are fertile and appear normal; however, they are haploinsufficient with regard to androgen action in Sertoli cells. In contrast, Arip4 / embryos are not viable. They have significantly reduced body size at E9.5 and die by E11.5. Compared to wild-type littermates, Arip4 / embryos possess a higher percentage of apoptotic cells at E9.5 and E10.5. Fibroblasts derived from Arip4 / embryos cease growing after 2-3 passages and exhibit a significantly increased apoptosis and decreased proliferation rate than cells from wild-type embryos. Our findings demonstrate that ARIP4 plays an essential role in mouse embryonic development. In addition, testicular expression and AR coregulatory activity of ARIP4 suggest a role of ARIP4-AR interaction in the somatic cells of the testis.

Orphan nuclear receptor subfamily NR4A their interplay with other nuclear receptors and functions in osteoblasts

Nurr1, NGFI-B and Nor1 (NR4A2, NR4A1 and NR4A3, respectively) belong to the NR4A subfamily of nuclear receptors. The NR4A receptors are orphan nuclear receptors which means that activating or repressing ligands for these receptors have not been found. NR4A expression is rapidly induced in response to various stimuli including growth factors and the parathyroid hormone (PTH). The studies concerning the NR4A receptors in the central nervous system have demonstrated that they have a major role in the development and function of the dopaminergic neurons of the midbrain and in regulating hypothalamus-pituitary-adrenal-axis. However, the peripheral functions of the NR4A family are largely unknown. Cultured mouse primary osteoblasts, a preosteoblastic cell line and several osteoblastic cell lines were used to investigate the role of NR4A receptors in osteoblasts. NR4A receptors were shown to directly bind to and activate the promoter of the osteopontin gene (OPN) in osteoblastic cells, thus regulating its expression. OPN is a major bone matrix protein expressed throughout the differentiation of preosteoblastic cells into osteoblasts. The activation of the OPN promoter was shown to be dependent on the activation function-1 located in the N-terminal part of Nurr1 and to occur in both monomeric and RXR heterodimeric forms of NR4A receptors. Furthermore, PTH was shown to upregulate OPN expression through the NR4A family. It was also demonstrated that the fibroblast growth factor-8b (FGF-8b) induces the expression of NR4A receptors in osteoblasts as immediate early genes. This induction involved phosphatidylinositol-3 kinase, protein kinase C, and mitogen activated protein kinase, which are all major pathways of FGF signalling. Nurr1 and NGFI-B were shown to induce the proliferation of preosteoblastic cells and to reduce their apoptosis. FGF-8b was shown to stimulate the proliferation of osteoblastic cells through the NR4A receptors. These results suggest that NR4A receptors have a role both in the differentiation of osteoblasts and in the proliferation and apoptosis of preosteoblast. The NR4A receptors were found to bind to the same response element on OPN as the members of the NR3B family of orphan receptors do. Mutual repression was observed between the NR4A receptors and the NR3B receptors. This repression was shown to be dependent on the DNA-binding domains of both receptor families, but to result neither from the competition of DNA binding nor from the competition for coactivators. As the repression was dependent on the relative expression levels of the NR4As and NR3Bs, it seems likely that the ratio of the receptors mediates their activity on their response elements. Rapid induction of the NR4As in response to various stimuli and differential expression of the NR3Bs can effectively control the gene activation by the NR4A receptors. NR4A receptors can bind DNA as monomers, and Nurr1 and NGFI-B can form permissive heterodimers with the retinoid X receptor (RXR). Permissive heterodimers can be activated with RXR agonists, unlike non-permissive heterodimers, which are formed by RXR and retinoic acid receptor or thyroid hormone receptor (RAR and TR, respectively). Non-permissive heterodimers can only be activated by the agonists of the heterodimerizing partner. The mechanisms behind differential response to RXR agonists have remained unresolved. As there are no activating or repressing ligands for the NR4A receptors, it would be important to find out, how they are regulated. Permissiviness of Nurr1/RXR heterodimers was linked to the N-terminal part of Nurr1 ligand-binding domain. This region has previously been shown to mediate the interaction between NRs and corepressors. Non-permissive RAR and TR, permissive Nurr1 and NGFI-B, and RXR were overexpressed with corepressors silencing mediator for retinoic acid and thyroid hormone receptors (SMRT), and with nuclear receptor corepressor in several cell lines. Nurr1 and NGFI-B were found to be repressed by SMRT. The interaction of RXR heterodimers with corepressors was weak in permissive heterodimers and much stronger in non-permissive heterodimers. Non-permissive heterodimers also released corepressors only in response to the agonist of the heterodimeric partner of RXR. In the permissive Nurr1/RXR heterodimer, however, SMRT was released following the treatment with RXR agonists. Corepressor release in response to ligands was found to differentiate permissive heterodimers from non-permissive ones. Corepressors were thus connected to the regulation of NR4A functions. In summary, the studies presented here linked the NR4A family of orphan nuclear receptors to the regulation of osteoblasts. Nurr1 and NGFI-B were found to control the proliferation and apoptosis of preosteoblasts. The studies also demonstrated that cross-talk with the NR3B receptors controls the activity of these orphan receptors. The results clarified the mechanism of permissiviness of RXR-heterodimers. New information was obtained on the regulation and functions of NR4A receptors, for which the ligands are unknown.

The Functions and Regulation of Ornithine Decarboxylase

Ornithine decarboxylase (ODC) regulates the synthesis of polyamines which are involved in many cellular functions e.g. proliferation and differentiation. Due to its critical role, ODC is a tightly regulated enzyme by antizymes and antizyme inhibitors. If the regulation fails, the activity of ODC increases and may lead to malignant transformation of a cell. Increased ODC activity is found in many common cancers, including colon, prostate, and breast cancer. In a transformed cell, dynamics of the actin cytoskeleton is disturbed. A small G-protein, RhoA regulates organization of the cytoskeleton, and its overactivity increases malignant potential of the cell. The present results indicate that covalent attachment of polyamines by transglutaminase is a physiological means of regulating the activity of RhoA. The translocation of RhoA to the plasma membrane, where it exerts its activity is dependent on the presence of catalytically active ODC. As the overactivity of ODC and RhoA are implicated in cell transformation, the results provide a mechanistic explanation of the interrelationship between the polyamine metabolism and the reorganization of the actin cytoskeleton occurring in cancer cells. ODC and polyamines have also an important role in the function of central nervous system. They participate in the regulation of brain morphogenesis in embryos. In adult nervous tissue, polyamines regulate K+ and glutamate channels. K+ inward rectifying channels control membrane potentials and NMDA-type glutamate receptors (NMDAR) regulate synaptic plasticity. High ODC activity and polyamine levels are considered important in the development of ischemic brain damage and they are implicated in the pathogenesis of Alzheimer s disease (AD). A homolog of ODC was cloned from a human brain cDNA library, and several alternatively spliced variants were detected in human brain and testis. The novel protein was nevertheless devoid of ODC catalytic activity. It was subsequently found to be a novel inductor of ODC activity and polyamine synthesis, called antizyme inhibitor 2 (AZIN2). The accumulation of AZIN2 in vesicle-like formations along the axons and beneath the plasma membrane of neurons as well as in steroid hormone producing Leydig cells and luteal cells of the gonads implies that AZIN2 plays a role in secretion and vesicle trafficking. An accumulation of AZIN2 was detected also in specimens of AD brains. This increased expression of AZIN2 was specific for AD and was not found in brains with other neurodegenerative diseases including CADASIL or dementia with Lewy bodies.

Application of the method of initial functions for the analysis of composite laminated plates

The method of initial functions has been applied for deriving higher order theories for cross-ply laminated composite thick rectangular plates. The equations of three-dimensional elasticity have been used. No a priori assumptions regarding the distribution of stresses or displacements are needed. Numerical solutions of the governing equations have been presented for simply supported edges and the results are compared with available ones.

p53 and little brother p53/47: linking IRES activities with protein functions

The tumor suppressor p53 represents a paradigm for gene regulation. Its rapid induction in response to DNA damage conditions has been attributed to both increased half-life of p53 protein and also increased translation of p53 mRNA. Recent advances in our understanding of the post-transcriptional regulation of p53 include the discovery of internal ribosome entry sites (IRESs) within the p53 mRNA. These IRES elements regulate the translation of the full length as well as the N-terminally truncated isoform, p53/47. The p53/47 isoform is generated by alternative initiation at an internal AUG codon present within the p53 ORF. The aim of this review is to summarize the role of translational control mechanisms in regulating p53 functions. We discuss here in detail how diverse cellular stress pathways trigger alterations in the cap-dependent and cap-independent translation of p53 mRNA and how changes in the relative expression levels of p53 isoforms result in more differentiated p53 activity.

Latent TGF-beta Binding Proteins : Adhesive functions and matrix association of LTBP-2 and potential functions of LTBP-1 and LTBP-3 in mesothelioma

Latent transforming growth factor-beta (TGF-beta) binding proteins (LTBPs) -1, -3 and -4 are ECM components whose major function is to augment the secretion and matrix targeting of TGF-beta, a multipotent cytokine. LTBP-2 does not bind small latent TGF-beta but has suggested functions as a structural protein in ECM microfibrils. In the current work we focused on analyzing possible adhesive functions of LTBP-2 as well as on characterizing the kinetics and regulation of LTBP-2 secretion and ECM deposition. We also explored the role of TGF-beta binding LTBPs in endothelial cells activated to mimic angiogenesis as well as in malignant mesothelioma. We found that, unlike most adherent cells, several melanoma cell lines efficiently adhered to purified recombinant LTBP-2. Further characterization revealed that the adhesion was mediated by alpha3beta1 and alpha6beta1 integrins. Heparin also inhibited the melanoma cell adhesion suggesting a role for heparan sulphate proteoglycans. LTBP-2 was also identified as a haptotactic substrate for melanoma cell migration. We used cultured human embryonic lung fibroblasts to analyze the temporal and spatial association of LTBP-2 into ECM. By We found that LTBP-2 was efficiently assembled to the ECM only in confluent cultures following the deposition of fibronectin (FN) and fibrillin-1. In early, subconfluent cultures it remained primarily in soluble form after secretion. LTBP-2 colocalized transiently with FN and fibrillin-1. Silencing of fibrillin-1 expression by lentiviral shRNAs profoundly disrupted the deposition of LTBP-2 indicating that the ECM association of LTBP-2 depends on a pre-formed fibrillin-1 network. Considering the established role of TGF-beta as a regulator of angiogenesis we induced morphological activation of endothelial cells by phorbol 12-myristate 13-acetate (PMA) and followed the fate of LTBP-1 in the endothelial ECM. This resulted in profound proteolytic processing of LTBP-1 and release of latent TGF-beta complexes from the ECM. The processing was coupled with increased activation of MT-MMPs and specific upregulation of MT1-MMP. The major role of MT1-MMP in the proteolysis of LTBP-1 was confirmed by suppressing the expression with lentivirally induced short-hairpin RNAs as well as by various metalloproteinases inhibitors. TGF-beta can promote tumorigenesis of malignant mesothelioma (MM), which is an aggressive tumor of the pleura with poor prognosis. TGF-beta activity was analyzed in a panel of MM tumors by immunohistochemical staining of phosphorylated Smad-2 (P-Smad2). The tumor cells were strongly positive for P-Smad2 whereas LTBP-1 immunoreactivity was abundant in the stroma, and there was a negative correlation between LTBP-1 and P-Smad2 staining. In addition, the high P-Smad2 immunoreactivity correlated with shorter survival of patients. mRNA analysis revealed that TGF-beta1 was the most highly expressed isoform in both normal human pleura and MM tissue. LTBP-1 and LTBP-3 were both abundantly expressed. LTBP-1 was the predominant isoform in established MM cell lines whereas the expression of LTBP-3 was high in control cells. Suppression of LTBP-3 expression by siRNAs resulted in increased TGF-beta activity in MM cell lines accompanied by decreased proliferation. Our results suggest that decreased expression of LTBP-3 in MM could alter the targeting of TGF-beta to the ECM and lead to its increased activation. The current work emphasizes the coordinated process of the assembly and appropriate targeting of LTBPs with distinct adhesive or cytokine harboring properties into the ECM. The hierarchical assembly may have implications in the modulation of signaling events during morphogenesis and tissue remodeling.

Adriamycin affects plasma membrane redox functions

Adriamycin (Doxorubicin) stimulates NADH oxidase activity in liver plasma membrane, but does not cause NADH oxidase activity to appear where it is not initially present, as in erythrocyte membrane. NADH dehydrogenase from rat liver and erythrocyte plasma membranes shows similar adriamycin effects with other electron acceptors. Both NADH ferricyanide reductase and vanadate-stimulated NADH oxidation are inhibited by adriamycin, as is a cyanide insensitive ascorbate oxidase activity, whereas NADH cytochrome c reductase is not affected. The effects may contribute to the growth inhibitory (control) and/or deleterious effects of adriamycin. It is clear that adriamycin effects on the plasma membrane dehydrogenase involve more than a simple catalysis of superoxide formation.

Molecular biology and functions of epilysin (MMP-28)

Epilysin (MMP-28) is the most recently identified member of the matrix metalloproteinase (MMP) family of extracellular proteases. Together these enzymes are capable of degrading almost all components of the extracellular matrix (ECM) and are thus involved in important biological processes such as development, wound healing and immune functions, but also in pathological processes such as tumor invasion, metastasis and arthritis. MMPs do not act solely by degrading the ECM. They also regulate cell behavior by releasing growth factors and biologically active peptides from the ECM, by modulating cell surface receptors and adhesion molecules and by regulating the activity of many important mediators in inflammatory pathways. The aim of this study was to define the unique role of epilysin within the MMP-family, to elucidate how and when it is expressed and how its catalytic activity is regulated. To gain information on its essential functions and substrates, the specific aim was to characterize how epilysin affects the phenotype of epithelial cells, where it is biologically expressed. During the course of the study we found that the epilysin promoter contains a well conserved GT-box that is essential for the basic expression of this gene. Transcription factors Sp1 and Sp3 bind this sequence and could hence regulate both the basic and cell type and differentiation stage specific expression of epilysin. We cloned mouse epilysin cDNA and found that epilysin is well conserved between human and mouse genomes and that epilysin is glycosylated and activated by furin. Similarly to in human tissues, epilysin is normally expressed in a number of mouse tissues. The expression pattern differs from most other MMPs, which are expressed only in response to injury or inflammation and in pathological processes like cancer. These findings implicate that epilysin could be involved in tissue homeostasis, perhaps fine-tuning the phenotype of epithelial cells according to signals from the ECM. In view of these results, it was unexpected to find that epilysin can induce a stable epithelial to mesenchymal transition (EMT) when overexpressed in epithelial lung carcinoma cells. Transforming growth factor b (TGF-b) was recognized as a crucial mediator of this process, which was characterized by the loss of E-cadherin mediated cell-cell adhesion, elevated expression of gelatinase B and MT1-MMP and increased cell migration and invasion into collagen I gels. We also observed that epilysin is bound to the surface of epithelial cells and that this interaction is lost upon cell transformation and is susceptible to degradation by membrane type-1-MMP (MT1-MMP). The wide expression of epilysin under physiological conditions implicates that its effects on epithelial cell phenotype in vivo are not as dramatic as seen in our in vitro cell system. Nevertheless, current results indicate a possible interaction between epilysin and TGF-b also under physiological circumstances, where epilysin activity may not induce EMT but, instead, trigger less permanent changes in TGF-b signaling and cell motility. Epilysin may thus play an important role in TGF-b regulated events such as wound healing and inflammation, processes where involvement of epilysin has been indicated.

Novel insights on functions of myotilin/palladin family members

Poikkijuovaisen luuranko- ja sydänlihaksen supistumisyksikkö, sarkomeeri, koostuu tarkoin järjestyneistä aktiini- ja myosiinisäikeistä. Rakenne eroaa muista solutyypeistä, joissa aktiinisäikeistö muovautuu jatkuvasti ja sen järjestyminen säätelee solun muotoa, solujakautumista, soluliikettä ja solunsisäisten organellien kuljetusta. Myotilin, palladin ja myopalladin kuuluvat proteiiniperheeseen, jonka yhteispiirteenä ovat immunoglobuliinin kaltaiset (Igl) domeenit. Proteiinit liittyvät aktiinitukirankaan ja niiden arvellaan toimivan solutukirangan rakenne-elementteinä ja säätelijöinä. Myotilinia ja myopalladinia ilmennetään poikkijuovaisessa lihaksessa. Sen sijaan palladinin eri silmukointimuotoja tavataan monissa kudostyypeissä kuten hermostossa, ja eri muodoilla saattaa olla solutyypistä riippuvia tehtäviä. Poikkijuovaisessa lihaksessa kaikki perheen jäsenet sijaitsevat aktiinisäikeitä yhdistävässä Z-levyssä ja ne sitovat Z-levyn rakenneproteiinia, -aktiniinia. Myotilingeenin pistemutaatiot johtavat periytyviin lihastauteihin, kun taas palladinin mutaatioiden on kuvattu liittyvän periytyvään haimasyöpään ja lisääntyneeseen sydäninfarktin riskiin. Tässä tutkimuksessa selvitettin myotilinin ja pallainin toimintaa. Kokeissa löydettiin uusia palladinin 90-92kDa alatyyppiin sitoutuvia proteiineja. Yksi niistä on aktiinidynamiikkaa säätelevä profilin. Profilinilla on kahdenlaisia tehtäviä; se edesauttaa aktiinisäikeiden muodostumista, mutta se voi myös eristää yksittäisiä aktiinimolekyylejä ja edistää säikeiden hajoamista. Solutasolla palladinin ja profilinin sijainti on yhtenevä runsaasti aktiinia sisältävillä solujen reuna-alueilla. Palladinin ja profilinin sidos on heikko ja hyvin dynaaminen, joka sopii palladinin tehtävään aktiinisäideiden muodostumisen koordinoijana. Toinen palladinin sitoutumiskumppani on aktiinisäikeitä yhteensitova -aktiniini. -Aktiniini liittää solutukirangan solukalvon proteiineihin ja ankkuroi solunsisäisiä viestintämolekyylejä. Sitoutumista välittävä alue on hyvin samankaltainen palladinissa ja myotilinissa. Luurankolihaksen liiallinen toistuva venytys muuttaa Z-levyjen rakennetta ja muotoa. Prosessin aikana syntyy uusia aktiinifilamenttejä sisältäviä tiivistymiä ja lopulta uusia sarkomeereja. Löydöstemme perusteella myotilinin uudelleenjärjestyminen noudattaa aktiinin muutoksia. Tämä viittaa siihen, että myotilin liittää yhteen uudismuodostuvia aktiinisäikeitä ja vakauttaa niitä. Myotilin saattaa myös ankkuroida viesti- tai rakennemolekyylejä, joiden tehtävänä on edesauttaa Z-levyjen uudismuodostusta. Tulostemme perusteella arvelemme, että myotilin toimii Z-levyjen rakenteen vakaajana ja aktiinisäikeiden säätelijänä. Palladinin puute johtaa sikiöaikaiseen kuolemaan hiirillä, mutta myotilinin puutoksella ei ole samanlaisia vaikutuksia. Tuotettujen myotilin poistogeenisten hiirten todetiin syntyvän ja kehittyvän normaalisti eikä niillä esiintynyt rakenteellisia tai toiminnallisia häiriöitä. Toisaalta aiemmissa kokeissa, joissa hiirille on siirretty ihmisen lihastautia aikaansaava myotilingeeni, nähdään samankaltaisia kuin sairailla ihmisillä. Näin ollen muuntunut myotilin näyttä olevan lihaksen toiminnalle haitallisempi kuin myotilinin puute. Myotilinin ja palladinin yhteisvaikutusta selvittääksemme risteytimme myotilin poistegeenisen hiiren ja hiirilinjan, joka ilmentää puutteellisesti palladinin 200 kDa muotoa. Puutteellisesti 200 kDa palladinia ilmentävien hiirten sydänlihaksessa todettiin vähäisiä hienorakenteen muutoksia, mutta risteytetyillä hiirillä tavattiin rakenteellisia ja toiminnallisia muutoksia myös luurankolihaksessa. Tulosten perusteella voidaan todeta, että palladinin 200 kDa muoto säätelee sydänlihassolujen rakennetta. Luurankolihaksessa sen sijaan myotilinilla ja palladinilla näyttäisi olevan päällekkäisiä tehtäviä.

Anisochrony of O-methylene protons of ethyl ester functions and structural factors in the connected chiral entities

(i) Incistrans pairs of cyclic 1,3-dicarboxylic acid ethyl esters thecis-foms exhibit higher O-methylene proton (HA, HB) anisochrony than thetrans-forms; (ii) anisochrony, easily observed in certain decalin-10-carboxylic ethyl esters, ‘disappears’ on one of the rings attaining the possibility of transforming into a ‘twist’ form; (iii) in certain pairs of chiralsecethyl esters and theirtert-methylated analogues anisochrony is higher in the latter, contrary to expectation, while, in certain others, the reverse is observed. Attempted explanations are based on assessments whether H A and H B are or are not in highly different magnetic environments in confomers regarded as preferred. This subsumes the possibility thatXYZC-CO2H A H B Me chiral ethyl acetates differ fromXYZC-CH A H B Me ethanes because intervention by the carboxyl group insulates the prochiral centre and allows anisotropic effects to gain somewhat in importance among mechanisms that discriminate between H A and H B so long as rotamerpopulation inequalities persist. Background information on why rotamer-population inequalities will always persist and on a heuristic that attempts to generalize the effects ofXYZ inXYZC - CU AUB V is provided. Possible effects when connectivity exists between a pair amongX, Y, Z or when specific interactions occur betweenV andX, Y orZ are considered. An interpretation in terms of ‘increasing conformational mobility’ has been suggested for the observed increase in the rate of temperature-dependence of O-methylene anisochrony down a series of chiral ethyl esters.

Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.