Purity of the Ideal of Continuous Functions with Compact Support

&#60;P&#62;Let C(X) be the ring of all continuous real valued functions defined on a completely regular T1-space. Let CK(X) be the ideal of functions with compact support. Purity of CK(X) is studied and characterized through the subspace XL, the set of all points in X with compact neighborhoods (nbhd). It is proved that CK(X) is pure if and only if XL=&#8746;f&#8712;CK supp f. if CK(X) and CK(Y) are pure ideals, then CK(X) is isomorphic to CK(Y) if and only if XL is homeomorphic to YL. It is proved that CK(X) is pure and XL is basically disconnected if and only if for every f &#8712;CK(X), the ideal (f ) is a projective C(X)-module. Finally it is proved that if CK(X) is pure, then XL is an F'-space if and only if every principal ideal of CK(X) is a flat C(X)-module. Concrete examples exemplifying the concepts studied are given.</p

Structure of the isotropic transport operators in three independent space variables

Based on the idea of separation of variables, a spectral theory for the three-dimensional, stationary, isotropic transport operator in a vector space of complex-valued Borel functions results in continuous sets of regular and generalized eigenfunctions

Low-Floor Tanner Codes via Hamming-Node or RSCC-Node Doping

We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the “doping” of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good” graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult. Lastly, we perform a simple complexity analysis of our Tanner codes and examine the performance of lower-complexity, suboptimal Hamming-node decoders

Remittances and Economic Growth: Empirical Evidence from Bangladesh India and Sri Lanka

In many developing countries, remittance payments from migrant workers are increasingly becoming a significant source of export income. This paper investigates the causal link between remittances and economic growth in three countries, Bangladesh, India and Sri Lanka, by employing the Granger causality test under a VAR framework (Granger 1988). Using time series data over a 25 year period, we found that growth in remittances does lead to economic growth in Bangladesh. In India, there seems to be no causal relationship between growth in remittances and economic growth; but in Sri Lanka, a two-way directional causality is found; namely economic growth influences growth in remittences and vice-versa. The paper also discusses a number of policy issues arising from the results of the analysis in relation to remittances in association with liberalisation of financial institutions, gender issues, regulation and enforcement, investment and savings schemes, and promotion and education.

FAQchat as in Information Retrieval system

A chatbot is a conversational agent that interacts with users through natural languages. In this paper, we describe a new way to access information using a chatbot. The FAQ in the School of Computing at the University of Leeds has been used to retrain the ALICE chatbot system, producing FAQchat. The results returned from FAQchat are similar to ones generated by search engines such as Google. For evaluation, a comparison was made between FAQchat and Google. The main objective is to demonstrate that FAQchat is a viable alternative to Google and it can be used as a tool to access FAQ databases

Continuous Spin Representations from Group Contraction

We consider how the continuous spin representation (CSR) of the Poincare group in four dimensions can be generated by dimensional reduction. The analysis uses the front-form little group in five dimensions, which must yield the Euclidean group E(2), the little group of the CSR. We consider two cases, one is the single spin massless representation of the Poincare group in five dimensions, the other is the infinite component Majorana equation, which describes an infinite tower of massive states in five dimensions. In the first case, the double singular limit j,R go to infinity, with j/R fixed, where R is the Kaluza-Klein radius of the fifth dimension, and j is the spin of the particle in five dimensions, yields the CSR in four dimensions. It amounts to the Inonu-Wigner contraction, with the inverse K-K radius as contraction parameter. In the second case, the CSR appears only by taking a triple singular limit, where an internal coordinate of the Majorana theory goes to infinity, while leaving its ratio to the KK radius fixed.Comment: 22 pages; some typos correcte

Sediment phosphorus flux in Beaver Lake in Northwest Arkansas

Internal phosphorus (P) loading may influence primary production in lakes, but the influence of sediment-derived P has not been well studied in Beaver Lake of Northwest Arkansas. Soluble reactive phosphorus (SRP), dissolved organic P (DOP), and total dissolved P (TDP) sediment-water fluxes were determined using intact sediment cores collected from deepwater environments in the riverine, transition zone, and lacustrine zones of Beaver Lake. The SRP, DOP, and TDP fluxes were also estimated from cores collected from shallow locations in the transition zone. There was a net positive SRP (0.001 – 0.005 µg P cm-2 h-1), DOP (0.005 – 0.01 µg P cm-2 h-1), and TDP (0.005 – 0.01 µg P cm-2 h-1) flux from deepwater sediments into the water column. However, DOP and TDP flux in shallow sediments were net negative (-0.004 and -0.002 µg P cm-2 h-1, respectively), suggesting that the majority of P was moving from water into sediment. The SRP flux from shallow sediments in the transition zone was similar to rates observed in deepwater sediments (0.002 µg P cm-2 h-1). However, the variability among flux rates, sites and depths was high, and therefore no statistical differences were found. Sediment oxygen demand was positively correlated with SRP and DOP flux rates from shallow transition zone sediments suggesting that microbial biomass and activity may have influenced sediment P flux. The P flux from shallow sediments supports approximately 1% to 5% of the daily P demand of phytoplankton. When compared to other lakes, sediment P flux in Beaver Lake appears minimal and is probably not an effective avenue to manage eutrophication in this system

Immune checkpoints in circulating and tumor-Infiltrating CD4 + T Cell Subsets in Colorectal cancer patients

Blockade of inhibitory immune checkpoints (ICs) is a promising therapeutic approach; however, it has shown limited success in some cancers including colorectal cancer (CRC). The tumor microenvironment (TME) is largely responsible for response to therapy, and its constituents may provide robust biomarkers for successful immunotherapeutic approaches. In this study, we performed phenotypical characterization and critical analyses of key inhibitory ICs and T regulatory cell (Treg)-related markers on CD4+ T cell subsets in CRC patients, and compared with normal colon tissues and peripheral blood from the same patients. We also investigated correlations between the levels of different CD4+ T cell subsets and the clinicopathologic features including disease stage and tumor budding. We found a significant increase in the levels of CD4+FoxP3+Helios+ T cells, which represent potentially highly immunosuppressive Tregs, in the CRC TME. Additionally, tumor-infiltrating CD4+ T cells upregulated programmed cell death protein-1 (PD-1), cytotoxic T-lymphocyte-associated protein-4 (CTLA-4), T cell immunoglobulin and mucin domain-3 (TIM-3) and lymphocyte-activation gene 3 (LAG-3). We also characterized the expression of PD-1, CTLA-4, TIM-3, and LAG-3 on different CD4+FoxP3−/+Helios−/+ T cell subsets. Interestingly, we found that CTLA-4, TIM-3, and LAG-3 were mainly co-expressed on FoxP3+Helios+ Tregs in the TME. Additionally, FoxP3high Tregs expressed higher levels of Helios, CTLA-4 and TIM-3 than FoxP3low T cells. These results highlight the significance of Tregs in the CRC TME and suggest that Tregs may hamper response to IC blockade in CRC patients, but effects of different IC inhibition regimes on Treg levels or activity warrants further investigations. We also found that CD4+CTLA-4+ T cells in circulation are increased in patients with advanced disease stage. This study simultaneously provides important insights into the differential levels of CD4+ T cell subpopulations and IC expression in CRC TME, compared to periphery and associations with clinicopathologic features, which could be used as potential biomarkers for CRC progression and response to therapy