L2 Type Research Articles

Ratio Limit Theorems for Self-Adjoint Operators and Symmetric Markov Chains

A simplest ratio limit theorem is obtained for self-adjoint operators in the spaces of L2 type which leave invariant a cone of nonnegative elements. By means of the theorem we establish ratio limit theorems for symmetric Markov chains and symmetric kernels in measurable spaces. In particular, it is shown that for symmetric Harris recurrent Markov chains a result is valid which is an analogue of the known Orey theorem (1961) about discrete recurrent symmetric chains. Similar statements are valid for nonnegative symmetric quasi-Feller kernels on locally compact spaces which are Liouville in a certain sense.

Finite Dimensional Approximations to Wiener Measure and Path Integral Formulas on Manifolds

Certain natural geometric approximation schemes are developed for Wiener measure on a compact Riemannian manifold. These approximations closely mimic the informal path integral formulas used in the physics literature for representing the heat semi-group on Riemannian manifolds. The path space is approximated by finite dimensional manifolds HP(M) consisting of piecewise geodesic paths adapted to partitions P of [0, 1]. The finite dimensional manifolds HP(M) carry both an H1 and a L2 type Riemannian structures, G1P and G0P, respectively. It is proved that (1/ZiP)e−(1/2)E(σ)dVolGiP(σ)→ρi(σ)dν(σ) as mesh (P)→0, where E(σ) is the energy of the piecewise geodesic path σ∈HP(M), and for i=0 and 1, ZiP is a “normalization” constant, VolGiP is the Riemannian volume form relative to GiP, and ν is Wiener measure on paths on M. Here ρ1(σ)≡1 and ρ0(σ)=exp(−16∫10Scal(σ(s))ds) where Scal is the scalar curvature of M. These results are also shown to imply the well known integration by parts formula for the Wiener measure.

EFFECT OF THE SURFACTANT ON ENZYMATIC HYDROLYSIS OF PALM OIL IN MICROEMULSION

ABSTRACT Lipase catalyzed hydrolysis of a triglyceride, palm oil, was performed in L2 type microemulsions based on different surfactants. Isooctane was used as hydrocarbon and the composition of the microemulsions was the same in all experiments. NMR self-diffusion measurements indicated that all microemulsions consisted of closed water droplets and that the structure did not change much during the course of the reaction. The hydrolysis was fast in the microemulsions based on branched-chain anionic or nonionic surfactant but very slow when a branched cationic or a linear nonionic surfactant was used. The cationic surfactant was found to form aggregates with the enzyme. No such interactions were detected with the other surfactants.

Response properties of stained monopolar cells in the honeybee lamina

1. Monopolar cells of the first visual ganglion, the lamina, of the bee were recorded from and stained intracellularly. 2. Several different response types to pulses of spectral light were found. The most common response type hyperpolarized in a phasic-tonic fashion. The tonic hyperpolarizing response frequently decreased gradually, but in some cases increased with lasting illumination. Some cells also gave a transient response to light-OFF. In contrast, one stained and several unstained cells showed depolarizing responses. Five cells exhibited spiking responses under normal physiological conditions. 3. The V/log I-functions were steeper than those of the photoreceptors and, in some cases, had both rising and falling parts with increasing intensities. The spectral sensitivity obtained with the constant response method showed a peak in the green (510–535 nm) in most cells. A series of spectral flashes revealed an additional type with highest sensitivity in UV. Indirect evidence was found in one cell for spectral opponent processing. 4. Two morphological types of monopolar cells were stained. These correspond well to Ribi's (1976) L1 and L2 cells, with some differences in detail. The most frequently stained cell type closely resembles his L2 type. All 3 stained spiking cells were of this type.

Pre-B Acute Lymphoblastic Leukemia During a Complete Remission in T-Acute Lymphoblastic Leukemia.

This case provides evidence for a phenotypic switch from a characteristic T-ALL into a typical pre-B ALL. A 17 years old boy presented with massive hepatosplenomegaly and a mediastinal mass. The blasts were characterized as L2 type according to the French, American and British (FAB) classification and the staining with acid phosphatase was positive. The immunophenotype was CD2 +, CD5 +, CD7 + and CD10 -. The patient achieved a complete remission but relapsed 4 years later. At relapse, a striking immunological shift was apparent. The blast cells were now morphologically LI subtype and displayed the CD10 +. C{mew} + phenotype but were CD2 -, CD5 -, CD7 -. These findings are consistent with a transformation of the initial clone although the development of a second leukemia in the same patient could not be excluded with complete certainty.

Late-appearing Philadelphia chromosome in acute lymphoblastic leukemia

We describe the cytogenetic analysis of a patient affected by a common acute lymphoblastic leukemia, L2 type. At diagnosis and first relapse, the karyotype was normal, whereas at the second relapse more than 60% of the examined cells showed a Philadelphia chromosome, without any change in the morphological and immunophenotypical picture. This case confirms the observation that leukemic cells are susceptible to developing a Ph, considered a primary chromosomal abnormality, during the course of the disease.

Trisomy 4 in a case of acute biphenotypic leukemia

Trisomy 4 was the sole chromosome anomaly in a 5-year-old girl with acute leukemia. Morphologically, there appeared to be distinct myeloid and lymphoid blast cells on presentation. Immunophenotyping, however, showed extensive overlap of myeloid and lymphoid markers, confirming the leukemia to be biphenotypic rather than true "bilineal." She attained remission only after lymphoid-cell-specific induction was added to the initial "myeloid type" induction. She relapsed 4 years later with morphologically acute lymphocytic leukemia (French-American-British L2 type) despite still retaining the original immunophenotypic characteristics. She was successfully reinduced and subsequently received an autologous bone marrow transplant. Second relapse, morphologically and immunophenotypically similar to the first, occurred 5 months after transplant.

An acute granular lymphoid leukemia with unusual cytochemistry and immunologic phenotype

A 15-year-old Mexican boy presented with an L2 type acute lymphoid leukemia (ALL). Occasional granulated and hand mirror cells were observed, and enzyme histochemistry showed the blasts to be positive for acid phosphatase, beta glucuronidase, and alpha napthyl butyrate esterase. Immunologic studies showed the cells to stain for terminal deoxynucleotidyl transferase and common ALL antigen and to react with B4 (90 per cent), B1 (60 per cent), and B2 (37 per cent) monoclonal antibodies. T-cell-associated antigens (T1, T4, T6, T8, T11) were present in only 10 per cent or less of the cells. Monoclonal antibodies for granulocytes and monocytes were negative. Surface immunoglobulin was absent. Chromosome studies showed a normal phenotype. Clinically, the patient did well, achieving a remission on a high risk ALL protocol. The case shows a marked dichotomy between enzyme histochemistry and immunologic monoclonal antibody markers and is an unusual case of granulated hand mirror lymphoblastic leukemia of pre-B cell origin.

Differences in the sensitivity of protocerebral neurosecretory cells arising from the effect of different factors in Morimus funereus larvae

1. 1.The combined effect of different factors (temperature, starvation, potassium saline, cerebral complex extract) on the activity of protocerebral neurosecretory cells (A1, A2, L2) in Morimus funereus larvae has been studied. 2. 2.Our results show that the most sensitive cells to the effect of the factors studied are A1 cells, and the least sensitive ones are those of L2 type. The latter respond mainly to the effect of potassium saline as well as to the cerebral complex extract, changing the affinity of the cytoplasm and neurosecretory granules from paraldehyde fuchsin positive into orange G positive, in addition to other parameters. 3. 3.Variability among larvae regarding the activity of medial neurosecretory cells, particularly of the most sensitive ones (A1 types), has been observed, both under natural and experimental conditions.

Acute Leukemic Infiltration of the Vitreous Diagnosed by Pars Plana Aspiration

A 30-year-old man with acute lymphoblastic leukemia, null cell, L2 type developed a unilateral dense cellular vitreous infiltrate while in apparent remission. Cytopathologic examination of material aspirated from the vitreous established the diagnosis of lymphoblastic infiltration. Prompt radiotherapy and chemotherapy rapidly reduced the vitreous infiltration and cleared cells from the cerebrospiral fluid. Intraocular involvement by the leukemic process was the initial sign of central nervous system involvement. Acute lymphoblastic leukemia should be added to the list of lymphoproliferative disorders capable of vitreous infiltration, and which can be identified by vitreous aspiration and cytopathologic examination.

Subclassification of acute lymphoblastic leukaemia in children: analysis of the reproducibility of morphological criteria and prognostic implications.

Stained smears of aspirated bone marrow obtained at time of diagnosis from 223 children with acute leukaemia were reviewed independently by three observers in a double-blind fashion in order to assess the reproducibility and clinical significance of the French-American-British Cooperative Group Classification. In 170 cases of acute lymphoblastic leukaemia (ALL), triple agreement of 69.4% was reached in the subclassification into L1, L2, and L3 types. The closest degree of agreement between two observers was 86.8%. In children with blasts classified as L1, 57 OF 61 patients (93.4%) remained in haematological remission after 12 months, as compared with 14 of 20 (70%) in children whose blasts were typed as L2 morphology, a difference which was statistically significant (P less than 0.05). There was no difference when these groups were compared after 24 or 36 months. Children older than 7 years had an increased incidence of L2 type (P less than 0.05). We conclude that although there may be significant variation in individual interpretations of the criteria utilized for classification, blast morphology may nevertheless be a useful prognostic factor.

Acute non myeloid leukaemia in adults. Prognostic factors in 92 patients.

An analysis of prognostic factors was performed on a series of 92 adult patients with acute non-myeloid leukaemia (ANML). Four factors were shown to be correlated with a poor short-term prognosis: (1) Neuropathy involving a single cranial nerve (numbness of the chin) as a presenting feature. (2) A low percentage blast cell infiltration of bone marrow (less than 55%). (3) Cytological L2 type or L3 type of cells according to FAB classification proposals. (4) Increased age. Two factors were shown to be correlated with a poor long-term prognosis: 1) A high level of circulating blast cells; 2) A high tumour burden, as in childhood ANML. These two long-term prognostic factors were interrelated. In addition, our results suggested that myelofibrosis could be a poor long-term prognosis factor as well.

Kinetics of the addition reactions of tetracyanoethylene to MX(CO)L2 (M = rhodium, iridium) type complexes

Kinetics of the addition reactions of tetracyanoethylene to MX(CO)L2 (M = rhodium, iridium) type complexes

Removal of viruses from water by sorption on coal

The objective of this research was to investigate the potential of bituminous coal as sorbent for removing viruses from water and to delineate the sorption mechanism(s). This study was undertaken in view of the increasing use of coal in water and wastewater treatment. Bacteriophage T4 against Escherichia coli BB was used as a model virus and coal samples from Neyveli and Giridih were used as sorbents. A sampling method for rapid separation of unsorbed viruses from the sorbent was standardized which consisted of filtering the sample containing coal and viruses through a Whatman filter paper soaked in beef extract. Effects of the following parameters on virus sorption were investigated: pH, ionic strength, temperature, and presence of proteinaceous matter. Maximum virus sorption (about 70%) was observed at pH 8·0 with input virus concentration 1·44 × 10 4 PFU ml −1, coal size 350 μm and ionic strength 0·02. Optimum ionic strength for virus sorption was found to be 0·015. Higher temperatures increased the sorption capacity and the activation energy was found to be 30·3 kcal/mole. This and low desorption values (6–10%) suggested irreversible chemisorption. Effect of carbon content of coal on sorption-desorption was studied using pure graphite which showed negligible desorption. Effect of proteinaceous matter was investigated using 5% domestic wastewater and the culture broth. Proteinaceous matter appeared to compete with virus for sorption sites on coal and reduced sorption by about 12%. Kinetics and equilibria of sorption on Neyveli coal at pH values 5·5, 7·1 and 8·0 were studied in a non-flow agitated system. Equilibrium sorption was attained in 90 min, the bulk of it being over in 45 min. Sorption data followed Langmuir type isotherm plots and suggested L2 type plot according to Gile's classification ( J. Chem. Soc. Part 3, p. 3973, 1960). Isotherm plot with 5% domestic wastewater gave an S curve, suggesting moderate to large intermolecular attraction and implying strong competition for substrate sites from molecules of the solvent. Monomolecular coverage to the extent of only 0·1% of total surface area agreed with the assumptions of isotherm plot and penetration into micropores and macropores of coal was ruled out.

Evaluación experimental y matemática de modelos de adsorción molecular para contaminantes orgánicos en partículas de TiO2-P25

Se evaluaron modelos convencionales de adsorción molecular basados en isotermas del tipo L2 para compuestos orgánicos ácido dicloroacético, fenol y 4-clorofenol sobre partículas de TiO2-25 a diferentes condiciones de operación. Los modelos estudiados fueron Langmuir-Hinshelwood, Redlich-Petersen y Toth puesto que estos modelos pueden ser aplicados como posibles ecuaciones para mejorar la descripción de los mecanismos de velocidad de reacción basados en ataque de radicales hidroxilo y degradación usando fotocatálisis heterogénea. Los modelos fueron comparados con datos experimentales para determinar la isoterma más adecuada. El modelo L-H fue el mas apropiado y los resultados fueron de alta efectividad en la predicción de los datos experimentales