Conditions For Embedding Research Articles

Conditions for embeddability of semigroups in groups

We call the words A i and B i defining words. We assume that all defining words are different. We call words of x 1 . . . . . x n without negative powers (including the null word) positive words. By a cusp with respect to (1) we mean a word X for which, for some U l, U 2, V1, and V 2, the words U1XU 2 and VIXV 2 are defining words, and either U 1 ~ U 2 or V l ;~ V 2. The small cancellation condition Cs(p) for (1) is the condition that no defining word is the product of less than p cusps. Following S.I. Adyan [2, 3], we introduce the notions of left and right graphs for the corepresentation (1) (see also [4]). The vertices of both left and right graphs are the letters of the alphabet x 1, x 2 . . . . . x n. For each i E I, we consider the arc ei (/) of the left graph that connects the initial letters of the words A i and B i. Similarly, the arc ei (r) of the right graph connects the final letters of these words. The small cancellation condition D(q) for (1) is the condition that neither the left nor right graphs has cycles with less than q arcs. We say that a semigroup S satisfies the left (right) cancellation condition if, for any x, y, z E S, xy = xz (yx = zx) implies that y = z. If S satisfies both conditions, we say that S is a semigroup with cancellation. The classes Kpq were studied in [1]. By definition, a semigroup S belongs to the class Kpq if it can be specified by a corepresentation (1) that satisfies the small cancellation conditions Cs(P) and D(q). We now recall some results. Adyan [2, 3] proved that all semigroups of the class K1 ~ = tqq Klq, i.e., semigroups without cycles, are embeddable in groups. In [5] Mal'tsev constructed an example of a semigroup with cancellation that belongs to the class K22 but is not embeddable in a group. An even simpler examples was presented in [2]. Such a semigroup is specified by the corepresentation (a, b, c, d, e Iab = cd, aeb =ced) . One of the fundamental results of [1] is Theorem 4.1, which asserts that semigroups of the classes K42 and K33 are embeddable in groups. On the other hand, for all q > 2, Kashintsev [1] constructed examples of semigroups of the classes K2q that are not embeddable in groups. The following two problems were stated in [1]: 1) Are all semigroups that belong to the class I(32 embeddable in groups? 2) Are there semigroups with cancellation in the classes K2q that are not embeddable in groups for q > 2? We answer both of these questions here. We state our fundamental results as follows.

Radial solutions to a nonlinear p-harmonic dirichlet problem

We examine the nonlinear ordinary differential equation corresponding to radial solutions of the Dirichlet problem .It is shown that for p and q satisfying the subcritical Sobolev embedding condition, the problem exhibits infinitely many solutions.Several properties of these solutions are presented, includingdetailed regularity results.

Semistable measures and limit theorems on real andp-adic groups

For any locally compact groupG, we show that any locally tight homomorphism from a real directed semigroup intoM 1 (G) (semigroup of probability measures onG) has a ‘shift’ which extends to a continuous one-parameter semigroup. IfG is ap-adic algebraic group then the above holds even iff is not locally tight. These results are applied to give sufficient conditions for embeddability of some translate of limits of sequences of the form {v } and μ∈M 1 (G) such that τ(μ)=μ M , for somek>1 and τ∈AutG (cf. Theorems 2.1, 2.4, 3.7).

Subcellular calcium localization in Toxoplasma gondii by electron microscopy and by X‐ray and electron energy loss spectroscopies

The localization of calcium in Toxoplasma gondii tachyzoites was studied at the ultrastructural level, with a cytochemical pyroantimonate precipitation method (PA) and controlled by EGTA chelating and EDX and EELS microanalyses. Appropriate conditions for material preparation, fixation and embedding, were defined. The proportion of precipitates that were either free or inside vacuoles and their distribution inside Toxoplasma appeared to be PA dose-dependent. Precipitation mainly occurred in the anterior pole of the Epon-embedded tachyzoites. EDX and EELS analyses showed that out of 30 PA precipitates inside tachyzoites, 78% contained Ca. In Melamine sections, 96% of the tachyzoites had intracellular precipitates and the membrane complex was stained; 25% of the tachyzoites inside host cells contained PA-Ca precipitates, but most of them were retained in the reticular network of the parasitophorous vacuole. Melamine embedding appeared to improve the preservation of calcium pyroantimonate precipitates.

Light-like CR hypersurfaces of indefinite K�hler manifolds

We study a new class of real hypersurfaces called ‘Light-like CR hypersurfaces’, of indefinite Kahler manifolds, and claim several new results of geometrical/physical significance. In particular, we show that our study has a direct relation with the physically important asymptotically flat spacetimes; which further lead to the Twistor theory of Penrose and the Heaven theory of Newman. As the induced connection, on the degenerate hypersurface, may not be a metric connection, we overcome this difficulty by using differential geometric technique and deduce the embedding conditions called Gauss-Codazzi equations. Finally, we find the integrability conditions for all the possible distributions and specialize the embedding conditions when the ambient space is a complex space form. We add to the list of totally umbilical nondegenerate hypersurfaces [16] the totally umbilical light-like cone, in the degenerate case, and prove the nonexistence of totally umbilical light-like CR hypersurfaces in ¯M(c) withc ≠ 0 (see Yano and Kon [22] and Tashiro and Tachibana [20] for the nondegenerate case).

Methods for Electrophoretic Karyotyping of Filamentous Fungi in the Genus Trichoderma

Methods for electrophoretic karyotyping of filamentous fungi in the genus Trichoderma were developed. These techniques permitted the separation and visualization of intact chromosomes from viable protoplasts. Three strains were analyzed: Trichoderma harzianum strains T12 his − 2 and T95 lys − 1, and a protorophic strain (1295-22) produced by protoplast fusion of T12 his − 2 with T95 lys − 1. Four chromosome bands ranging in size from 2.2 Mb (megabase pairs) to 5.4 Mb were visualized with strain T95 lys − 1, whereas two chromosome bands were visualized for strains T12 his − 2 and 1295-22. The largest chromosome of all three strains seems to be similar in size and has been estimated to be approximately 5.4 Mb. All remaining chromosomes observed were dissimilar in size. Methods for protoplast isolation, protoplast embedding, and electrophoretic conditions useful for separation of intact chromosomes ranging in size from 50 kb (kilobase pairs) up to approximately 6.0 Mb utilizing transverse alternating field electrophoresis (TAFE) will be discussed. The techniques provided should be applicable to a variety of lower eukaryotic organisms when using the TAFE system.

Embeddings of weighted Sobolev spaces into spaces of continuous functions

We give sufficient conditions and necessary conditions (which in some cases are both necessary and sufficient) for continuous and compact embeddings of the weighted Sobolev space W 1,p ( Ω ;v 0 v 1 )into spaces of weighted continuous and Holder continuous functions. The theoretical results are illustrated by several examples.

Quantum-well diode frequency multipliers: varistor case

Local oscillators for heterodyne receivers at submillimeter wavelengths are typically made using a fundamental source followed by a harmonic frequency multiplier. An investigation of the required circuit embedding conditions for a possible new harmonic generator, the quantum-well resonant-tunneling diode, is summarized. A low-frequency multiplier has been tested that employs the resistive nonlinearity of the device as opposed to the reactive nonlinearity. The results show good agreement between practice and theory. >

Structure - function relationships in heterogeneous catalysis: replacing the asterisk

A new concept for describing the active site in heterogeneous catalysis, called the embedded surface molecule, is defined. The surface molecule consists of the atoms from reagent, catalyst and product which participate directly in the catalytic act. Embedding considers the relationship of the surface molecule to the rest of the catalyst. Embedding modifies the electronic environment of the surface molecule and also provides reagent molecules to the site by surface diffusion. The concept is illustrated by reference to the catalytic oxidation of carbon monoxide at the Rh(110) surface. Two different types of kinetics are observed, depending on the oxygen coverage and it is argued that the changeover is largely due to a change in embedding conditions, while the reacting surface molecule is unchanged.

Evidence that the capsule around mycobacteria grown in axenic media contains mycobacterial antigens: implications at the level of cell envelope architecture

The intracellular growth of pathogenic mycobacteria has been linked to the presence of an electron transparent zone (ETZ or capsule), which surrounds the phagocytized bacteria and prevents the diffusion of lysosomal enzymes in infected macrophages. Recently, it was suggested that this capsule may be a bacterial structures, even being present in test tube-grown pathogenic mycobacteria (FEMS Microbiol. Lett. 1988, 56, 225-230). In the present paper, we show that under special fixation and embedding conditions, this capsule was clearly observed among 7 strains of mycobacteria grown in axenic media and also in M. leprae extracted and purified from experimentally infected armadillo or nude mice. In the case of bacteria treated likewise but subject to a prior dehydration step, this capsular structure disappeared suggesting its lipidic nature. Ultrathin sections of M. intracellular after immunolabelling showed for the first time that this capsule obtained mycobacterial antigens confirming its mycobacterial origin. It is suggested that the mycobacterial capsule may be formed of inert lipids, in which surface antigens are embedded.

The Crystalline Cluster Method for Ionic Solids. The F Center in NaCl

AbstractThe electronic structure of the F center in sodiun chloride is investigated by the multiple scattering Xα method with proper crystalline embedding conditions. Several different clusters are used in order to determine the influence of the choice of the muffin‐tin radii and Xα parameters on the cluster energy spectrum. The calculated value of the first absorption line is compared with the experimental results and other theoretical work. It is found that the results obtained agree very well with experiment, provided clusters with at least 27 atoms are used in the calculation.

Elliptically embedded subgroups and nilpotent products

A recent paper of Rhemtulla and Wilson [4] is concerned with elliptically embedded subgroups of groups. A subgroup H of a group G is elliptically embedded in G if, for each subgroup K of G, there is some integer m such that (H, K) = (HK)m. Some sufficient conditions for elliptic embedding are given in Section 2 of [4], and some consequences of the presence of this property are to be found in Theorems 1 and 2 of the same paper and in the main theorem of [5]. It is evident from all of these results that the property of being elliptically embedded is closely related to the nilpotency and subnormality of certain subgroups. One of the questions considered here i s the following.

Fundamental Equations for Submanifolds

We notice that in the embedding of submanifolds, the fundamental equations are only the Gauss equations for the tangent vectors while the Weingarten equations for the normal equations can essentially be determined by them, and furthermore that the integrability condition of the Weingarten equations, the Ricci equations, are consitently satisfied under that of the Gauss equations. Therefore, the Weingarten and the Ricci equations do not describe essentially independent conditions for embedding. We demonstrate these facts by explicitly constructing the normal vectors from the tangent vectors.

Study of RNA distribution in the nucleolar components of Ehrlich cell using RNase-gold method.

The RNA distribution in Ehrlich tumour cell nucleoli has been investigated using RNase-gold method. This technique has been applied to sections of cells prepared under various fixation and embedding conditions. As expected, the specificity and intensity of labelling by gold particles have varied according to the experimental conditions used. Interestingly, however, it has been noted that the localization of gold particles does also vary and in particular within the fibrillar centre. This observation underlines the interest of assaying the RNase-gold complex under various conditions. The gold particles were particularly concentrated over the granular component and to a lesser extent, in the dense fibrillar component. In the latter constituent, it has been noted that the gold markers were preferentially localized at the edge of the dense fibrils. Surprisingly, a few gold particles have also been detected in the fibrillar centres. The weak labelling has persisted even after pepsin or DNase extraction but has completely disappeared after RNase extraction. Further, an inhibition of rRNA synthesis by a treatment with actinomycin D has not produced a significant decrease of the number of gold particles present in the fibrillar centre. These results suggest that fibrillar centres contain a small amount of RNA which would not correspond to pre-rRNA.

Identification of serotonergic neurons in human brain by a monoclonal antibody binding to all three aromatic amino acid hydroxylases

A monoclonal antibody, PH8, has been isolated and shown by immunocytochemistry to bind to serotonergic and catecholaminergic neurons in sections of the rat and human brain. In human brain, obtained at autopsy, particular fixation and embedding conditions eliminate the labelling of catecholaminergic neurons while leaving intact the labelling of serotonergic neurons. This property makes the antibody of potential use for structural studies of serotonergic neurons in the normal and diseased human brain. PH8 was raised to pure monkey phenylalanine hydroxylase and has been shown to bind to the 50,000 mol. wt. phenylalanine hydroxylase polypeptide. Immunocytochemical and immunochemical evidence is presented in support of the hypothesis that the labelling of serotonergic and catecholaminergic neurons results from the binding of PH8 to tryptophan and tyrosine hydroxylase, respectively.

Effect of tissue processing on colloidal gold cytochemistry.

The aim of cytochemical techniques is to localize specific biochemical components in particular tissue and cell compartments. However, since preparation of tissues for structural observation results in major alterations of the properties of their components, a major problem is to retain an adequate degree of their biochemical properties as well as adequate structural preservation. In the present study, we describe results obtained using various colloidal gold cytochemical techniques on tissues processed through different approaches. We found that any manipulation of the tissue during its processing can result in modifications of tissue components, leading to problems in cytochemistry. Indeed, washing of the tissue before fixation, the nature of the fixative solution, the chemical basis of the resins, and the physical conditions of embedding can all introduce changes in tissue components which can be cytochemically demonstrated. This has been illustrated with application of the protein A-gold, lectin-gold, and enzyme-gold cytochemical techniques on tissues submitted to different processings: fixation by perfusion or by immersion; glutaraldehyde vs paraformaldehyde fixative solutions; cryo-ultramicrotomy; embedding in epoxy, GMA, Lowicryl, or LR resins. The results obtained have demonstrated that conditions for optimal labeling must be worked out for each class of binding sites, and that no single procedure can be recommended as THE best approach in cytochemistry.

Immunogold labeling of CMP-KDO synthetase produced by recombinant E. Coli cells

CMP-KDO synthetase (CKS) is an enzyme which plays a key role in the synthesis of LPS, an outer membrane component unique to gram negative bacteria. CKS activates KDO to CMP-KDO for incorporation into LPS. The enzyme is normally present in low concentrations (0.02% of total cell protein) which makes it difficult to perform large scale isolation and purification. Recently, the gene for CKS from E. coli was cloned and various recombinant DNA constructs overproducing CKS several thousandfold (unpublished data) were derived. Interestingly, no cytoplasmic inclusions of overproduced CKS were observed by EM (Fig. 1) which is in contrast to other reports of large proteinaceous inclusion bodies in various overproducing recombinant strains. The present immunocytochemical study was undertaken to localize CKS in these cells.Immune labeling conditions were first optimized using a previously described cell-free test system. Briefly, this involves soaking small blocks of polymerized bovine serum albumin in purified CKS antigen and subjecting them to various fixation, embedding and immunochemical conditions.

An artificial test substrate for evaluating electron microscopic immunocytochemical labeling reactions.

We describe an artificial substrate system for optimization of labeling parameters in electron microscope immunocytochemical studies. The system involves use of blocks of glutaraldehyde-polymerized BSA into which a desired antigen is incorporated by a simple soaking procedure. The resulting antigen-impregnated artificial substrate can then be fixed and embedded identically to a piece of tissue. The BSA substrate can also be dried and then sectioned for immunolabeling with or without chemical fixation and without exposing the antigen to dehydrating agents and embedding resins. The effects of various fixation and embedding procedures can thus be evaluated separately. Other parameters affecting immunocytochemical labeling, such as antibody and conjugate concentration, can also be evaluated. We used this system, along with immunogold labeling, to determine quantitatively the optimal fixation and embedding conditions for labeling of hepatitis B surface antigen (HbsAg), human IgG, and horseradish peroxidase. Using unfixed and unembedded HBsAg, we were able to detect antigen concentrations below 20 micrograms/ml. We have shown that it is not possible to label HBsAg within resin-embedded cells using conventional aldehyde fixation protocols and polyclonal antibodies.

Calabi-Yau manifold compactification in the heterotic string and N=1 supersymmetry in four dimensions

We examine whether a torsion-free Calabi-Yau manifold with the SU(3) holonomy group embedded in E 8×E 8 satisfies the classical field equations with O(α' 3) heterotic string corrections. In general, the torsion-freedom is lost and the exact embedding condition is modified at O(α' 3), but the N=1 supersymmetry in four dimensions is still preserved even at O(α' 3). Allowing some local field redefinitions, however, we can restore the exact embedding of the SU(3) holonomy into E 8×E 8→E 6×SU(3)×E 8, maintaining also the D=4, N=1 symmetry. Our results are based on the dual (type IB) superspace formulation, which guarantees the on-shell closure of supersymmetry.

Immunoelectron microscopic localization of D-amino acid oxidase in rat kidney and liver.

The intracellular localization of D-amino acid oxidase in rat kidney and liver has been investigated using the indirect immunogold postembedding technique. Different fixation and embedding conditions for optimal preservation of antigenicity and fine structure have been tested. Immunolabelling was possible only in tissues embedded in polar resins (glycol methacrylate and Lowicryl K4M). In kidney the enzyme was demonstrable only in the peroxisomes of the proximal tubule, where it was associated with the peroxisome core. The enzyme was present in all the peroxisomes of the proximal tubule and appeared to be codistributed with catalase. Control experiments and quantitative analysis confirmed the specificity of the D-amino acid oxidase immunolocalization. All the other cells in kidney failed to demonstrate any labelling. In liver, the immunolabelling was present in the matrix of the hepatocyte peroxisomes, whereas no traces of the enzyme were found in the nucleoid. The intensity of the immunolabelling in liver peroxisomes was lower than in kidney. No specific labelling was observed in cells other than hepatocytes.