Institute of Mathematics

Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory, other try to handle imprecision and uncertainty in different way. In this paper, we introduce a new notion of picture fuzzy sets (PFS), which are directly extensions of fuzzy sets and of intuitonistic fuzzy sets (Atanassov). Then some operations on picture fuzzy sets are defined and some properties of these operations are considered. Here the basic preliminaries of PFS theory are presented.

Research Article| April 01, 1997 Intraplate extension prior to continental extrusion along the Ailao Shan-Red River shear zone Sun-Lin Chung; Sun-Lin Chung 1Department of Geology, National Taiwan University, Taipei 106-17, Taiwan Search for other works by this author on: GSW Google Scholar Tung-Yi Lee; Tung-Yi Lee 2Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan Search for other works by this author on: GSW Google Scholar Ching-Hua Lo; Ching-Hua Lo 1Department of Geology, National Taiwan University, Taipei 106-17, Taiwan Search for other works by this author on: GSW Google Scholar Pei-Ling Wang; Pei-Ling Wang 1Department of Geology, National Taiwan University, Taipei 106-17, Taiwan Search for other works by this author on: GSW Google Scholar Chin-Yu Chen; Chin-Yu Chen 2Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan Search for other works by this author on: GSW Google Scholar Nguyen Trong Yem; Nguyen Trong Yem 3Institute of Geological Sciences, National Center for Natural Sciences and Technology, Hanoi, Vietnam Search for other works by this author on: GSW Google Scholar Tran Trong Hoa; Tran Trong Hoa 3Institute of Geological Sciences, National Center for Natural Sciences and Technology, Hanoi, Vietnam Search for other works by this author on: GSW Google Scholar Wu Genyao Wu Genyao 4Institute of Geology, Chinese Academy of Sciences, Beijing, China Search for other works by this author on: GSW Google Scholar Author and Article Information Sun-Lin Chung 1Department of Geology, National Taiwan University, Taipei 106-17, Taiwan Tung-Yi Lee 2Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan Ching-Hua Lo 1Department of Geology, National Taiwan University, Taipei 106-17, Taiwan Pei-Ling Wang 1Department of Geology, National Taiwan University, Taipei 106-17, Taiwan Chin-Yu Chen 2Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan Nguyen Trong Yem 3Institute of Geological Sciences, National Center for Natural Sciences and Technology, Hanoi, Vietnam Tran Trong Hoa 3Institute of Geological Sciences, National Center for Natural Sciences and Technology, Hanoi, Vietnam Wu Genyao 4Institute of Geology, Chinese Academy of Sciences, Beijing, China Publisher: Geological Society of America First Online: 02 Jun 2017 Online ISSN: 1943-2682 Print ISSN: 0091-7613 Geological Society of America Geology (1997) 25 (4): 311–314. https://doi.org/10.1130/0091-7613(1997)025<0311:IEPTCE>2.3.CO;2 Article history First Online: 02 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn Email Permissions Search Site Citation Sun-Lin Chung, Tung-Yi Lee, Ching-Hua Lo, Pei-Ling Wang, Chin-Yu Chen, Nguyen Trong Yem, Tran Trong Hoa, Wu Genyao; Intraplate extension prior to continental extrusion along the Ailao Shan-Red River shear zone. Geology 1997;; 25 (4): 311–314. doi: https://doi.org/10.1130/0091-7613(1997)025<0311:IEPTCE>2.3.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Left-lateral movement of the Ailao Shan–Red River shear zone lends support to the hypothesis of continental extrusion resulting from the collision of India with Asia. Our new observations from northwestern Yunnan, China, and northwestern Vietnam on different sides of the shear zone demonstrate that the sinistral offset was ∼600 km according to correlations of Permian-Triassic flood basalt successions and late Paleogene highly potassic mafic magmas. We conclude that the shear was propagating on the South China continental margin and does not correspond to a suture between South China and Indochina. Furthermore, the highly potassic magmas were emplaced from ca. 40 to 30 Ma, before the shear movement, which was caused by the late Oligocene to early Miocene (ca. 27–22 Ma) extrusion activity. This suggests that a late Eocene to early Oligocene intraplate extension, possibly induced by delamination of thickened continental lithosphere, took place in northwestern Yunnan (or eastern Tibet) as a response to the India-Asia collision. This extension, and sea-floor spreading of the South China Sea that began ca. 30 Ma, could have accounted for the initiation of the Ailao Shan–Red River shear zone. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Pisano and Pleitez have introduced an interesting SU(3${)}_{\mathit{C}}$ \ensuremath{\bigotimes} SU(3${)}_{\mathit{L}}$ \ensuremath{\bigotimes} U(1${)}_{\mathit{N}}$ gauge model which has the property that gauge anomaly cancellation requires the number of generations to be a multiple of 3. We consider generalizing that model to incorporate right-handed neutrinos. We find that there exists a nontrivial generalization of the Pisano-Pleitez model with right-handed neutrinos which is actually simpler than the original model in that symmetry breaking can be achieved with just three SU(3${)}_{\mathit{L}}$ triplets [rather than three SU(3${)}_{\mathit{L}}$ triplets and a sextet]. We also consider a gauge model based on SU(3${)}_{\mathit{C}}$ \ensuremath{\bigotimes} SU(4${)}_{\mathit{L}}$ \ensuremath{\bigotimes} U(1${)}_{\mathit{N}}$ symmetry. Both of these new models also have the feature that the anomalies cancel only when the number of generations is divisible by 3.

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.

BACKGROUND: Antimicrobial misuse is common in low-income and middle-income countries (LMICs), and this practice is a driver of antibiotic resistance. We compared community-based antibiotic access and use practices across communities in LMICs to identify contextually specific targets for interventions to improve antibiotic use practices. METHODS: We did quantitative and qualitative assessments of antibiotic access and use in six LMICs across Africa (Mozambique, Ghana, and South Africa) and Asia (Bangladesh, Vietnam, and Thailand) over a 2·5-year study period (July 1, 2016-Dec 31, 2018). We did quantitative assessments of community antibiotic access and use through supplier mapping, customer exit interviews, and household surveys. These quantitative assessments were triangulated with qualitative drug supplier and consumer interviews and discussions. FINDINGS: Vietnam and Bangladesh had the largest proportions of non-licensed antibiotic dispensing points. For mild illness, drug stores were the most common point of contact when seeking antibiotics in most countries, except South Africa and Mozambique, where public facilities were most common. Self-medication with antibiotics was found to be widespread in Vietnam (55·2% of antibiotics dispensed without prescription), Bangladesh (45·7%), and Ghana (36·1%), but less so in Mozambique (8·0%), South Africa (1·2%), and Thailand (3·9%). Self-medication was considered to be less time consuming, cheaper, and overall, more convenient than accessing them through health-care facilities. Factors determining where treatment was sought often involved relevant policies, trust in the supplier and the drug, disease severity, and whether the antibiotic was intended for a child. Confusion regarding how to identify oral antibiotics was revealed in both Africa and Asia. INTERPRETATION: Contextual complexities and differences between countries with different incomes, policy frameworks, and cultural norms were revealed. These contextual differences render a single strategy inadequate and instead necessitate context-tailored, integrated intervention packages to improve antibiotic use in LMICs as part of global efforts to combat antibiotic resistance. FUNDING: Wellcome Trust and Volkswagen Foundation.

We explore some more consequences of the SU(3${)}_{\mathit{L}}$\ensuremath{\bigotimes}U(1${)}_{\mathit{N}}$ electroweak model with right-handed neutrinos. By introducing the Z-Z\ensuremath{'} mixing angle \ensuremath{\varphi}, the exact physical eigenstates for neutral gauge bosons are4 obtained. Because of the mixing, there is a modification to the ${\mathit{Z}}^{1}$ coupling proportional to sin \ensuremath{\varphi}. The data from the Z decay allow us to fix the limit for \ensuremath{\varphi} as -0.0021\ensuremath{\leqslant}\ensuremath{\varphi}\ensuremath{\leqslant}0.000 132. From the neutrino neutral current scatterings, we estimate a bound for the new neutral gauge boson ${\mathit{Z}}^{2}$ mass in the range of 300 GeV, and from symmetry-breaking hierarchy a bound for the new charged and neutral (non-Hermitian) gauge bosons ${\mathit{Y}}^{\ifmmode\pm\else\textpm\fi{}}$, ${\mathit{X}}^{0}$ are obtained. \textcopyright{} 1996 The American Physical Society.

BACKGROUND: The irrational overuse of antibiotics should be minimized as it drives the development of antibiotic resistance, but changing these practices is challenging. A better understanding is needed of practices and economic incentives for antibiotic dispensing in order to design effective interventions to reduce inappropriate antibiotic use. Here we report on both quantitative and qualitative aspects of antibiotic sales in private pharmacies in northern Vietnam. METHOD: A cross-sectional study was conducted in which all drug sales were observed and recorded for three consecutive days at thirty private pharmacies, 15 urban and 15 rural, in the Hanoi region in 2010. The proportion of antibiotics to total drug sales was assessed and the revenue was calculated for rural and urban settings. Pharmacists and drug sellers were interviewed by a semi-structured questionnaire and in-depth interviews to understand the incentive structure of antibiotic dispensing. RESULTS: In total 2953 drug sale transactions (2083 urban and 870 rural) were observed. Antibiotics contributed 24% and 18% to the total revenue of pharmacies in urban and rural, respectively. Most antibiotics were sold without a prescription: 88% in urban and 91% in rural pharmacies. The most frequent reported reason for buying antibiotics was cough in the urban setting (32%) and fever in the rural area (22%). Consumers commonly requested antibiotics without having a prescription: 50% in urban and 28% in rural area. The qualitative data revealed that drug sellers and customer's knowledge of antibiotics and antibiotic resistance were low, particularly in rural area. CONCLUSION: Over the counter sales of antibiotic without a prescription remains a major problem in Vietnam. Suggested areas of improvement are enforcement of regulations and pricing policies and educational programs to increase the knowledge of drug sellers as well as to increase community awareness to reduce demand-side pressure for drug sellers to dispense antibiotics inappropriately.

Several strains of moderately halophilic and mesophilic bacteria were isolated at the head of an oil-producing well on an offshore platform in southern Vietnam. Cells were Gram-negative, non-spore-forming, rod-shaped and motile by means of a polar flagellum. Growth occurred at NaCl concentrations between 0 and 20%; the optimum was 5% NaCl. One strain, which was designated VT8T, could degrade n-hexadecane, pristane and some crude oil components. It grew anaerobically in the presence of nitrate on succinate, citrate or acetate, but not on glucose. Several organic acids and amino acids were utilized as sole carbon and energy sources. The major components of its cellular fatty acids were C12:0 3-OH, C16:1, omega 9c, C16:0 and C18:1 omega 9c. The DNA G + C content was 55.7 mol%. 16S rDNA sequence analysis indicated that strain VT8T was closely related to Marinobacter sp. strain CAB (99.8% similarity) and Marinobaster hydrocarbonoclasticus (99.4% similarity). Its antibiotic resistance, isoprenoid quinones and fatty acids were similar to those of Marinobacter hydrocarbonoclasticus and Pseudomonas nautica. However, the whole-cell protein pattern of VT8T differed from that of other halophilic marine isolates, including P. nautica. DNA-DNA hybridization indicated that the level of relatedness to Marinobacter hydrocarbonoclasticus was 65% and that to P. nautica was 75%. Further differences were apparent in Fourier-transformed IR spectra of cells and lipopolysaccharide composition. It is proposed that VT8T should be the type strain of a new species and should be named Marinobacter aquaeolei. P. nautica may have been misclassified, as suggested previously, and may also belong to the genus Marinobacter.

Hospital effluents represent an important source for the release of antibiotics and antibiotic resistant bacteria into the environment. This study aims to determine concentrations of various antibiotics in wastewater before and after wastewater treatment in a rural hospital (60 km from the center of Hanoi) and in an urban hospital (in the center of Hanoi) in Vietnam, and it aims to explore the relationship between antibiotic concentrations in wastewater before wastewater treatment and quantities of antibiotics used in the rural hospital, over a period of one year in 2013. Water samples were collected using continuous sampling for 24 h in the last week of every month. The data on quantities of antibiotics delivered to all inpatient wards were collected from the Pharmacy department in the rural hospital. Solid-phase extraction and high performance liquid chromatography-tandem mass spectrometry were used for chemical analysis. Significant concentrations of antibiotics were present in the wastewater both before and after wastewater treatment of both the rural and the urban hospital. Ciprofloxacin was detected at the highest concentrations in the rural hospital's wastewater (before treatment: mean = 42.8 µg/L; after treatment: mean = 21.5 µg/L). Metronidazole was detected at the highest concentrations in the urban hospital's wastewater (before treatment: mean = 36.5 µg/L; after treatment: mean = 14.8 µg/L). A significant correlation between antibiotic concentrations in wastewater before treatment and quantities of antibiotics used in the rural hospital was found for ciprofloxacin (r = 0.78; p = 0.01) and metronidazole (r = 0.99; p < 0.001).

A model based on the $\mathrm{SU}{(3)}_{L}\ensuremath{\bigotimes}\mathrm{U}{(1)}_{N}$ gauge group in which neutrinos have right-handed neutral currents is considered. We argue that in order to have a result consistent with the low-energy one, the right-handed neutrino component must be treated as a correction instead of an equivalent spin state.

Research Article| October 01, 1998 Thermochronological evidence for the movement of the Ailao Shan–Red River shear zone: A perspective from Vietnam Pei-Ling Wang; Pei-Ling Wang 1Department of Geology, National Taiwan University, Taipei, Taiwan Search for other works by this author on: GSW Google Scholar Ching-Hua Lo; Ching-Hua Lo 1Department of Geology, National Taiwan University, Taipei, Taiwan Search for other works by this author on: GSW Google Scholar Tung-Yi Lee; Tung-Yi Lee 2Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan Search for other works by this author on: GSW Google Scholar Sun-Lin Chung; Sun-Lin Chung 1Department of Geology, National Taiwan University, Taipei, Taiwan Search for other works by this author on: GSW Google Scholar Ching-Ying Lan; Ching-Ying Lan 3Institute of Earth Sciences, Academia Sinica, Taipei, Taiwan Search for other works by this author on: GSW Google Scholar Nguyen Trong Yem Nguyen Trong Yem 4Institute of Geological Sciences, National Center for Natural Sciences and Technology, Hanoi, Vietnam Search for other works by this author on: GSW Google Scholar Geology (1998) 26 (10): 887–890. https://doi.org/10.1130/0091-7613(1998)026<0887:TEFTMO>2.3.CO;2 Article history first online: 02 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share MailTo Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation Pei-Ling Wang, Ching-Hua Lo, Tung-Yi Lee, Sun-Lin Chung, Ching-Ying Lan, Nguyen Trong Yem; Thermochronological evidence for the movement of the Ailao Shan–Red River shear zone: A perspective from Vietnam. Geology 1998;; 26 (10): 887–890. doi: https://doi.org/10.1130/0091-7613(1998)026<0887:TEFTMO>2.3.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract In order to explore the timing of strike-slip movement along the Ailao Shan–Red River shear zone, an 40Ar/39Ar thermochronological study of the Day Nui Con Voi metamorphic massif in northern Vietnam was undertaken. The massif, exposed in the southeastern segment of the Ailao Shan–Red River shear zone, reveals a rapid cooling in the early Miocene (25–21 Ma) after a very slow cooling ca. 34–25 Ma. The slow cooling period most likely resulted from a geothermal perturbation in the lithosphere owing to the late Paleogene (40–30 Ma) extension in eastern Tibet and western Yunnan, China. The rapid cooling, consistent with evidence of a wider rapid cooling span from 27 to 17 Ma compiled from the entire Ailao Shan–Red River shear zone, constrains the duration of left-lateral shearing, which eventually offset Indochina from South China by about 600 km. The time constraints we have established reinforce the argument that the onset of the Ailao Shan–Red River shear zone postdates the opening of the South China Sea that began ca. 30 Ma. This result highlights the necessity for reevaluating the Cenozoic tectonic models of Southeast Asia. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

A generalization of the Zadeh's fuzzy sets and Antanassov's intuitionistic fuzzy - "Picture fuzzy set" have defined in 2013. This concept is particularly effective in decision making problems, such as voting, solutions choice, financial forecasting, estimating risks in business, etc. This promotes vigorously the construction of the picture fuzzy theory: 1) picture fuzzy operators on picture fuzzy sets, 2) picture fuzzy relations, 3) picture fuzzy soft sets. In this paper, we have investigated main fuzzy logic operators: negations, conjunctions, disjunctions and implications on picture fuzzy sets. As combined with picture fuzzy operators by De Morgan triples, we have also constructed main operations for fuzzy inference processes in picture fuzzy systems.

In this note a simple formula for the real stability radius of uncertain positive linear continuous time systems is established and it is shown that the real stability radius coincides with the complex one. Arbitrary disturbance norms induced by monotonic vector norms (e.g. p—norms) are considered. The distance of intervals of positive systems from instability is also determined

x * ∈ X is said to be an r-limit point of a sequence (xi ) in some normed linear space (X,∥ · ∥) if (r ≥ 0). The set of all r-limit points of (xi , denoted by LIM r x i , is bounded closed and convex. Further properties, in particular the relation between this rough convergence and other convergence notions, and the dependence of LIM r x i on the roughness degree r, are investigated. For instance, the set-valued mapping r ↦ LIM r x i is strictly increasing and continuous on (), where . For a so-called ρ-Cauchy sequence (xi ) satisfying it is shown in case X = R n that r = (n/(n + 1))ρ (or for Euclidean space) is the best convergence degree such that LIM r x i ≠ Ø.

Two probiotic strains, Lactobacillus agilis JCM 1048 and L. salivarius subsp. salicinius JCM 1230 isolated from chicken intestine, exhibited probiotic characteristics that can be applied for chicken production. After 7 days of probiotic feeding (FD7), the count of intestinal lactobacilli in the probiotic group (group P, n=10) was significantly (p<0.05) higher than that in the control group (group C, n=9). After 40 days of probiotic feeding (FD40), the lactobacilli and enterococci counts were stable but the Enterobacteriaceae number was significantly reduced (p<0.05). A total of 163 isolated lactobacilli were identified as the L. acidophilus/gallinarum group (49.7%), L. agilis (30.7%), L. salivarius (9.2%), L. reuteri (9.2%), and Lactobacillus spp. (1.2%). The probiotic lactobacilli positively affected the Lactobacillus biota in chickens at FD7, with a significant increase in the number (p<0.05) of L. agilis and group P. The viable counts of each Lactobacillus species at FD40, however, showed no differences between two groups. An increasing incidence of L. agilis was also noted with probiotic feeding. The probiotic effect of two strains resulted in significantly increased weight gains (10.7%) of group P in comparison with group C at FD40 (p<0.01).

Chemical research unveils the structure of chemical space, spanned by all chemical species, as documented in more than 200 y of scientific literature, now available in electronic databases. Very little is known, however, about the large-scale patterns of this exploration. Here we show, by analyzing millions of reactions stored in the Reaxys database, that chemists have reported new compounds in an exponential fashion from 1800 to 2015 with a stable 4.4% annual growth rate, in the long run neither affected by World Wars nor affected by the introduction of new theories. Contrary to general belief, synthesis has been the means to provide new compounds since the early 19th century, well before Wöhler's synthesis of urea. The exploration of chemical space has followed three statistically distinguishable regimes. The first one included uncertain year-to-year output of organic and inorganic compounds and ended about 1860, when structural theory gave way to a century of more regular and guided production, the organic regime. The current organometallic regime is the most regular one. Analyzing the details of the synthesis process, we found that chemists have had preferences in the selection of substrates and we identified the workings of such a selection. Regarding reaction products, the discovery of new compounds has been dominated by very few elemental compositions. We anticipate that the present work serves as a starting point for more sophisticated and detailed studies of the history of chemistry.

In this study, by using a characterisation of functions having a fractional derivative, the authors propose a rigorous fractional Lyapunov function candidate method to analyse the stability of fractional‐order nonlinear systems. First, they prove an inequality concerning the fractional derivatives of convex Lyapunov functions without the assumption of the existence of the derivative of pseudo‐states. Second, they establish fractional Lyapunov functions to fractional‐order systems without the assumption of the global existence of solutions. Their theorems fill the gaps and strengthen results in some existing papers.

For the problem of minimizing a concave function over a polytope a class of convergent algorithms is proposed, which is based upon a combination of the branch and bound technique with the cutting method developed earlier by H. Tuy.

We develop various (exact) calculus rules for Fréchet lower and upper subgradients of extended-real-valued functions in real Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima.

The chicken cecum contains a great many bacteria, most of which are strict anaerobes. A strictly anaerobe culture-based method was used in the present study, in conjunction with the 16S rDNA clone library, to elucidate bacterial diversity and the phylogenetic relationship of cecal microbiota in the chicken. A comparative 16S rDNA sequence analysis of cultivated strains and retrieved clones from cecal contents was performed. Approximately 90% of the bacterial cells detected by microscopy did not form colonies on a medium 10 in plate-in-bottle. The 19 isolated strains yielded 11 distinct rDNA sequences, 58% of which were classified as low G + C gram-positive bacteria, 26% were related to Bacteroides spp., and 16% were classified as Proteobacteria. Based on the sequence analysis of 164 clones, 24% were identified to belong to 8 known species and 76% were considered to be 65 novel phylotypes. Approximately 94% of cloned sequences were classified into low G + C gram-positive bacteria, 4% were related to Bacteroides spp., and 2% were classified into Proteobacteria. Clostridium subcluster XIVa (38%), Clostridium cluster IV (13%), Lactobacillus spp. (24%), and Bacteroides spp. (4%) were the major groups constituting the cecal microbiota in chicken, in which the Clostridium subcluster XIVa was the most phylogenetically diverse group in chicken cecum. The 16S rDNA sequences of Lactobacillus acidophilus, L. crispatus, L. salivarius, and L. reuteri were the most frequently found in the Lactobacillus group in chicken cecum.