Critical Point Methods Research Articles

Can respondent uncertainty be ignored when exploring heterogeneity in public preferences for air pollution treatment policies? Comparative results from choice experiment analysis

Based on choice experiment (CE), evaluating the public's heterogeneous preferences and willingness to pay (WTP) for air pollution treatment policies can provide useful social views for the reasonable formulation of treatment schemes. However, the application of CE contains an implicit assumption that respondents understand their real preferences and can make choices with complete certainty. In reality, for a variety of reasons, not all respondents are absolutely certain about their responses, this assumption distinctly is hard to be consistent with reality. To explore the impact of respondent uncertainty on the public's WTP and heterogeneous preferences for air pollution treatment policies, this study introduces the critical point and exponential weighting methods to deal with this uncertainty in the context of CE and conducts comparative analysis based on the random parameters logit (RPL) and latent classes models (LCM). The results show that, ignoring uncertainty leads to distortions in the public's WTP and preference characteristics. In the RPL models, on average, the WTP for attributes is overstated by 32.10%. Our results also reveal that, whether to consider uncertainty does not affect the ranking of the implicit prices of these attributes. After incorporating uncertainty into the analysis, respondents were divided into two potential groups with different preferences, namely the environment-focused group (79.44%) and the price-focused group (20.56%), which is quite distinct from research results of ignoring the uncertainty. Contribution of this study is not only to provide theoretical insights for exploring the effects of uncertainty on public preferences based on CE, but also to provide valuable guidance for policy makers to formulate more accurate and effective treatment measures.

Visualizing Planar and Space Implicit Real Algebraic Curves with Singularities

We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing space curve in higher-dimensional space. Since the topology of a curve near a singular point of it is not numerically stable, we trace only the curve outside neighborhoods of singular points and replace each neighborhood simply by a point, which produces a polygonal approximation that is $\epsilon$-close to the curve. Such an approximation is more stable for defining the numerical connectedness of the complement of the projection of the curve in $\mathbb{R}^2$, which is important for applications such as solving bi-parametric polynomial systems. The algorithm starts by computing three types of key points of the curve, namely the intersection of the curve with small spheres centered at singular points, regular critical points of every connected components of the curve, as well as intersection points of the curve with the given bounding box. It then traces the curve starting with and in the order of the above three types of points. This basic scheme is further enhanced by several optimizations, such as grouping singular points in natural clusters, tracing the curve by a try-and-resume strategy and handling "pseudo singular points". The effectiveness of the algorithm is illustrated by numerous examples. This manuscript extends our preliminary results that appeared in CASC 2018.

Requirements for stress gradient‐based fatigue assessment of notched structures according to theory of critical distance

AbstractNotches, local stress raisers within structural components, are one of the most important locations for fatigue crack initiation. It is well known that fatigue is governed by the effective stresses in the vicinity of notches. Within this study, differences in prediction accuracy between different types of theory of critical distance methods, that is, point and line methods, are systematically investigated in conjunction with a sensitivity study regarding mesh refinement, assumed strength hypothesis and material behaviour. For this purpose, a finite element analysis parameter study on notched structures is performed and recommendations for the application of stress gradient methods are presented. Difference in effective stress of up to 30%, and hence a significant difference in fatigue life (e.g., 185% for a slope of S‐N curve of k = 4), is found for typical notch shapes, for example, in welded joints.

PENGENDALIAN KUALITAS PANGAN DENGAN PENERAPAN GOOD MANUFACTURING PRACTICES (GMP) PADA PROSES PRODUKSI DODOL BETAWI (STUDI KASUS UKM MC)

Small and medium enterprise (SME) MC is a business in food industri which produces dodol betawi. Problems in the production process is using human who aren’t yet familiar with the attributes of cooking equipment as well as proper guidance in food production process. Workers haven’t recognized yet the importance of employee hygine regarding physical and bacterial hazards from the body so it doesn’t contaminate the food. The purpose of this study is to analyze the discrepancy of SME MC in implementing Good Manufacturing Practice (GMP) regulations so that discussing higher safety on products using the Failure Mode and Effect Analysis (FMEA) method can improve dodol food quality, and provide quality improvement.Based in laboratory tests of dodol betawi products, there are Escherichia coli bacteria provide evidence that storage errors in the drying process, when dodol already 1 week old, it causes the fungus Aspergillus flavus growth. The amount of Escherichia coli bacteria was found 25.000 bacteria/cc. The purpose of this research is to give improvement of sanitation operations standards for employee health in the production process of Dodol Betawi by using one of the Hazard Analysis and Critical Control Point (HACCP) methods, namely the application of Good Manufacturing Practice (GMP). The implementation of Good Manufacturing Practices (GMP) in this research is to provide cooking attribute equipment. The results of the implementation were able to reduce Escherichia coli bacteria by 10,000 bacteria / cc. The results of these improvements are expected to be able to make the MC UKM more trusted and widely known to the public. Keywords:  good manufacturing practice (GMP), failure mode and effect analysis (FMEA), laboratory test,         quality food

Bubble-resummation and critical-point methods for beta -functions at large N

We investigate the connection between the bubble-resummation and critical-point methods for computing the beta -functions in the limit of large number of flavours, N, and show that these can provide complementary information. While the methods are equivalent for single-coupling theories, for multi-coupling case the standard critical exponents are only sensitive to a combination of the independent pieces entering the beta -functions, so that additional input or direct computation are needed to decipher this missing information. In particular, we evaluate the beta -function for the quartic coupling in the Gross–Neveu–Yukawa model, thereby completing the full system at mathcal {O}(1/N). The corresponding critical exponents would imply a shrinking radius of convergence when mathcal {O}(1/N^2) terms are included, but our present result shows that the new singularity is actually present already at mathcal {O}(1/N), when the full system of beta -functions is known.

Sign-Changing and Multiple Solutions of Impulsive Boundary Value Problems Via Critical Point Methods

In this paper, we study the second-order impulsive boundary value problem ? Lu = f ( x , u ) , x ? [ 0 , 1 ] ? { x 1 , x 2 , ? , x l } , ? Δ ( p ( x i ) u ? ( x i ) ) = I i ( u ( x i ) ) , i = 1 , 2 , ? , l , R 1 ( u ) = 0 , R 2 ( u ) = 0 , $$\left\{\begin{array}{ll} -Lu=f(x, u), \, \, x\in [0, 1]\backslash\{x_{1}, x_{2}, \cdots, x_{l}\}, \\ -{\Delta} (p(x_{i}) u'(x_{i}))=I_{i}(u(x_{i})), \quad i=1, 2, \cdots, l, \\ R_{1}(u)=0, \, \, \, R_{2}(u)=0, \end{array}\right.$$ where Lu = (p(x)u?)? ? q(x)u is a Sturm-Liouville operator, R 1(u) = ?u?(0) ? βu(0) and R 2(u) = ?u?(1) + ?u(1). The existence of sign-changing and multiple solutions is obtained. The technical approach is based on minimax methods and invariant sets of descending flow.

From the Editors

From the Editors

Multiplicity results for Hammerstein integral equations via critical point theory

In this article we establish some multiplicity results for Hammerstein integral equations. The main results are based on critical point methods.

A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems

In this paper we present a framework which permits theunified treatment of the existence of multiple solutions forsuperlinear and sublinear Neumann problems. Using critical pointtheory, truncation techniques, the method of upper-lowersolutions, Morse theory and the invariance properties of thenegative gradient flow, we show that the problem can have sevennontrivial smooth solutions, four of which have constant sign andthree are nodal.

Risk Analysis of Hematopoietic Stem Cell Transplant Process: Failure Mode, Effect, and Criticality Analysis and Hazard Analysis Critical Control Point Methods Integration Based on Guidelines to Good Manufacturing Practice for Medicinal Product ANNEX 20 (February 2008)

The collection and handling of hematopoietic stem cells (HSCs) must meet high quality requirements. An integrated Quality Risk Management can help to identify and contain potential risks related to HSC production. Risk analysis techniques allow one to “weigh” identified hazards, considering the seriousness of their effects, frequency, and detectability, seeking to prevent the most harmful hazards. The Hazard Analysis Critical Point, recognized as the most appropriate technique to identify risks associated with physical, chemical, and biological hazards for cellular products, consists of classifying finished product specifications and limits of acceptability, identifying all off-specifications, defining activities that can cause them, and finally establishing both a monitoring system for each Critical Control Point and corrective actions for deviations. The severity of possible effects on patients, as well as the occurrence and detectability of critical parameters, are measured on quantitative scales (Risk Priority Number [RPN]). Risk analysis was performed with this technique on manipulation process of HPC performed at our blood center. The data analysis showed that hazards with higher values of RPN with greater impact on the process are loss of dose and tracking; technical skills of operators and manual transcription of data were the most critical parameters. Problems related to operator skills are handled by defining targeted training programs, while other critical parameters can be mitigated with the use of continuous control systems. The blood center management software was completed by a labeling system with forms designed to be in compliance with standards in force and by starting implementation of a cryopreservation management module.

Food Safety Issues: A Summary Report of a Panel Session Addressing Pre- and Post-Harvest Strategies to Improve Public Health

ABSTRACT The paper presents a summary of a panel presentation by animal scientists and public health veterinarians on food safety methods to improve public health of the public consuming beef and poultry. Pre-harvest methods discussed include vaccination to decrease shedding of Esherichia coli O157:H7, direct-fed microbials (DFMs), calving methods, and responsible use of antimicrobials. Post-harvest methods discussed include increased sampling and use of hazard analysis and critical control point (HACCP) methods, test-and-hold of meat products prior to release for public consumption, development of attainment categories, the use of pulsed field gel electrophoresis (PFGE) for genotyping and serotyping, and an 11-step surveillance program. The public health concern and financial consequences of contamination with E. coli O157:H7 is discussed. A “carrot and stick” approach for both producers and processors to increase vaccination and product testing is recommended.

Nonlinear difference equations investigated via critical point methods

The multiplicity of solutions for nonlinear difference equations involving the p -Laplacian is investigated. The approach is based on critical point theorems in the setting of finite dimensional Banach spaces.

Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term

We study the existence of solutions for the following nonlinear degenerate elliptic problems in a bounded domain Ω ⊂ R N \Omega \subset {{\mathbf {R}}^N} \[ − div ⁡ ( | ∇ u | p − 2 ∇ u ) = | u | p ∗ − 2 u + λ | u | q − 2 u , λ > 0 , - \operatorname {div} (|\nabla u{|^{p - 2}}\nabla u) = |u{|^{{p^{\ast }} - 2}}u + \lambda |u{|^{q - 2}}u,\qquad \lambda > 0, \] where p ∗ {p^{\ast }} is the critical Sobolev exponent, and u | δ Ω ≡ 0 u{|_{\delta \Omega }} \equiv 0 . By using critical point methods we obtain the existence of solutions in the following cases: If p > q > p ∗ p > q > {p^{\ast }} , there exists λ 0 > 0 {\lambda _0} > 0 such that for all λ > λ 0 \lambda > {\lambda _0} there exists a nontrivial solution. If max ( p , p ∗ − p / ( p − 1 ) ) > q > p ∗ \max (p,{p^{\ast }} - p/(p - 1)) > q > {p^{\ast }} , there exists nontrivial solution for all λ > 0 \lambda > 0 . If 1 > q > p 1 > q > p there exists λ 1 {\lambda _1} such that, for 0 > λ > λ 1 0 > \lambda > {\lambda _1} , there exist infinitely many solutions. Finally, we obtain a multiplicity result in a noncritical problem when the associated functional is not symmetric.

Three-dimensional morphology, ultrastructure, and replication of Mycoplasma felis.

The morphology and replication of Mycoplasma felis in relation to growth phase in culture were studied by electron microscopy. The organisms showed 1.0 to 1.45-hr doubling times with typical bacterial-type growth curves when grown in dialysate broth supplemented with horse serum. Organisms were fixed for electron microscopy by using Veronal acetate-buffered 0.8% OsO(4) (pH 6.1) in 20% sucrose. The morphology of exponential-phase organisms differed markedly from that of stationary or death-phase organisms, which were essentially large round forms with either dispersed or abnormally aggregated cytoplasm. Plasticine models prepared from serial sections of organisms in exponential phase showed the organisms to be either disc-shaped, triangular, horseshoe-shaped, or multilobular. A central "hole" was frequently present in these structures and could be visualized in the lobular forms as an interconnecting circular membrane. The inner surface of this membrane often showed contact with a small membranous body about 0.12 mum in diameter. The significance of this body is unknown. The morphology of the various shapes was confirmed by using the phosphotungstic acid and critical point methods. When the ratios of the various forms in exponential-phase cultures were determined, it was found that a replication sequence could be proposed which accounted for not only the volume increase required to accommodate deoxyribonucleic acid (DNA) replication but also the distribution of that DNA. Although it is likely that DNA replication in M. felis is a binary process, it appears that the mechanism for production of new cells need not be a binary process.