Non-critical Values Research Articles

Damped Perturbations of Systems with Center-Saddle Bifurcation

An autonomous system of ordinary differential equations on the plane with a center-saddle bifurcation is considered. The influence of a class of time damped perturbations is investigated. The particular solutions tending to the fixed points of the limiting system are considered. The stability of these solutions is analyzed by Lyapunov function method when the bifurcation parameter of the unperturbed system takes critical and noncritical values. Conditions that ensure the persistence of the bifurcation in the perturbed system are described. When the bifurcation is broken, a pair of solutions tending to a degenerate fixed point of the limiting system appears in the critical case. It is shown that, depending on the structure and the parameters of the perturbations, one of these solutions can be stable, metastable or unstable, while the other solution is always unstable. The proposed theory is applied to the study of autoresonance capturing in systems with quadratically varying driving frequency.

Algebraicity of the near central non-critical values of symmetric fourth L-functions for Hilbert modular forms

Let Π be a cohomological irreducible cuspidal automorphic representation of GL2(AF) with central character ωΠ over a totally real number field F. In this paper, we prove the algebraicity of the near central non-critical value of the symmetric fourth L-function of Π twisted by ωΠ−2. The algebraicity is expressed in terms of the Petersson norm of the normalized newform of Π and the top degree Whittaker period of the Gelbart–Jacquet lift Sym2Π of Π.

WALANT\u2013Epinephrine injection may lead to short term, reversible episodes of critical oxygen saturation in the fingertips

IntroductionAlthough the WALANT technique’s long-term safeness has been demonstrated in many studies, there are only few data investigating its short-term effects on tissue perfusion and oxygen levels. It was hypothesized that, temporarily, critical levels of tissue perfusion may occur.MethodsSeventeen patients, who were scheduled for different procedures in WALANT technique, were injected with 5–7 ml of 1% Articain containing 1:200,000 epinephrine at the finger base. Capillary-venous oxygen saturation, hemoglobin volume in the capillaries, and relative blood flow in the fingertips were recorded once per second by white light spectrometry and laser Doppler flowmetry before, during and after injection for an average of 32 min.ResultsClinically, no persistent tissue malperfusion was observed, and there were no postoperative complications. Capillary-venous oxygen saturation was reduced by ≥ 30% in seven patients. Critical levels of oxygen saturation were detected in four patients during 13 intervals, each lasting for 132.5 s on average. Oxygen saturation returned to noncritical values in all patients by the end of the observation period. Blood flow in the fingertips was reduced by more than 30% in nine patients, but no critical levels were observed, as with the hemoglobin. Three patients demonstrated a reactive increase in blood flow of more than 30% after injection.ConclusionsInjection of tumescent local anesthesia containing epinephrine into finger base may temporarily cause a substantial reduction in blood flow and lead to critical levels of oxygen saturation in the fingertips. However, this was fully reversible within minutes and does not cause long-term complications.

Cohort profile: the Alberta Prostate Cancer Research Initiative (APCaRI) Registry and Biorepository facilitates technology translation to the clinic through the use of linked, longitudinal clinical and patient-reported data and biospecimens from men in Alberta, Canada

PurposeThe Alberta Prostate Cancer Research Initiative (APCaRI) Registry and Biorepository was established in 2014 by the APCaRI to facilitate the collection of clinical and patient-reported data, biospecimen, to measure prostate...

Attitudes Sociales et Intellectuelles et Valeurs a Developper dans L'Enseignement Quebecois des Sciences Humaines au Primaire: Une Analyse des Propositions du Programme D'Etudes

Quebec's elementary school social studies program is part of an important movement in North American education. It promotes the development of politically correct social attitudes and scientifically correct intellectual attitudes that Orlandi (1971) called "socially acceptable attitudes." The authors, after identifying these attitudes, emphasize that, under the cover of a developmental approach in the area of savoiretre ("knowing how to be"), the program instead supports a techno behaviorist approach conducive to an approval of conformist and noncritical values and attitudes.

On higher regulators of Siegel threefolds II: the connection to the special value

We establish a connection between motivic cohomology classes over the Siegel threefold and non-critical special values of the degree-four$L$-function of some cuspidal automorphic representations of$\text{GSp}(4)$. Our computation relies on our previous work [On higher regulators of Siegel threefolds I: the vanishing on the boundary, Asian J. Math.19(2015), 83–120] and on an integral representation of the$L$-function due to Piatetski-Shapiro.

A real variety with boundary and its global parameterization

An algebraic variety in R3 is studied that plays an important role in the investigation of the normalized Ricci flow on generalized Wallach spaces related to invariant Einstein metrics. A procedure for obtaining a global parametric representation of this variety is described, which is based on the use of the intersection of this variety with the discriminant set of an auxiliary cubic polynomial as the axis of parameterization. For this purpose, elimination theory and computer algebra are used. Three different parameterization of the variety are obtained; each of them is valid for certain noncritical values of one of the parameters.

On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight

We study the asymptotics of recurrence coefficients for monic orthogonal polynomials $\pi_n(z)$ with the quartic exponential weight $\exp[-N(\frac 12 z^2+\frac 14 tz^4)]$, where $t\in {\mathbb C}$ and $N\in{\mathbb N}$, $N\to\infty$. Our goal is to describe these asymptotic behaviors globally for $t\in {\mathbb C}$ in different regions. We also describe the "breaking" curves separating these regions, and discuss their special (critical) points. All these pieces of information combined provide the global asymptotic "phase portrait" of the recurrence coefficients of $\pi_n(z)$, which was studied numerically in [Constr. Approx. 41 (2015), 529-587, arXiv:1108.0321]. The main goal of the present paper is to provide a rigorous framework for the global asymptotic portrait through the nonlinear steepest descent analysis (with the $g$-function mechanism) of the corresponding Riemann-Hilbert problem (RHP) and the continuation in the parameter space principle. The latter allows to extend the nonlinear steepest descent analysis from some parts of the complex $t$-plane to all noncritical values of $t$. We also provide explicit solutions for recurrence coefficients in terms of the Riemann theta functions. The leading order behaviour of the recurrence coefficients in the full scaling neighbourhoods the critical points (double and triple scaling limits) was obtained in [Constr. Approx. 41 (2015), 529-587, arXiv:1108.0321] and [Asymptotics of complex orthogonal polynomials on the cross with varying quartic weight: critical point behaviour and the second Painlev\'e transcendents, in preparation].

Regulators for Rankin–Selberg products of modular forms

We prove a weak version of Beilinson’s conjecture for non-critical values of L-functions for the Rankin–Selberg product of two modular forms.

The Patient Diarist in the Digital Age

The Patient Diarist in the Digital Age

Mean Field Equation of Liouville Type with Singular Data: Topological Degree

We consider the following mean field equation: urn:x-wiley::media:cpa21532:cpa21532-math-0001 where M is a compact Riemann surface with volume 1, h* is a positive C1 function on M, and ρ and αj are constants satisfying αj > −1. In this paper, we derive the topological‐degree‐counting formula for noncritical values of ρ. We also give several applications of this formula, including existence of the curvature + 1 metric with conic singularities, doubly periodic solutions of electroweak theory, and a special case of self‐gravitating strings. © 2015 Wiley Periodicals, Inc.

Topological classification of systems of Kovalevskaya-Yehia type

All the Fomenko-Zieschang invariants are calculated for the Kovalevskaya-Yehia problem, for all noncritical values of the parameters and , by constructing admissible systems of coordinates and determining the mutual disposition of the basis cycles. The family of Kovalevskaya-Yehia systems contains 29 pairwise Liouville non-equivalent foliations. These foliations include those that are equivalent to previously known foliations, which arose in the integrable cases of Kovalevskaya and of Kovalevskaya-Yehia for , in the Zhukovskiǐ case, and in the Goryachev-Chaplygin-Sretenskiǐ case. Eleven new foliations are included in the 29 foliations, new in the sense that they are not Liouville equivalent to any foliations discovered earlier which arose in the known integrable cases of the rigid body. The topological type of the Liouville foliation for the family of Kovalevskaya-Yehia systems stabilizes at large values of the energy , and this ‘high-energy’ system is roughly Liouville equivalent, at one of the energy levels, to the Goryachev-Chaplygin-Sretenskiǐ integrable case, which is already known.Bibliography: 29 titles.

Mock period functions in higher level cases

Generalizing the results of Bringmann, Diamantis and Raum [3] we investigate a generating series of non-critical values which can be interpreted as a mock period function and prove that non-critical values can be encoded into a sesquiharmonic Maass form in higher level cases. Moreover we prove Eichler–Shimura-type isomorphism for the space of period polynomials and for that of mock period functions in level p with p∈{2,3}.

Wavelet decomposition techniques and Hardy inequalities for function spaces on cubes

A rather tricky question is the construction of wavelet bases on domains for suitable function spaces (Sobolev, Besov, Triebel–Lizorkin type). In his monograph from 2008, Triebel presented an approach how to construct wavelet (Riesz) bases in function spaces of Besov and Triebel–Lizorkin type on cellular domains, in particular on the cube. However, he had to exclude essential exceptional values of the smoothness parameter s, for instance the theorems do not cover the Sobolev space W21(Q) on the n-dimensional cube Q for n≥2.Triebel also gave an idea how to deal with those exceptional values for the Triebel–Lizorkin function space scale on the n-dimensional cube Q: he suggested to introduce modified function spaces for the critical values, the so-called reinforced spaces which are subsets of the classical Triebel–Lizorkin function spaces on the cube. In this paper we start examining these reinforced spaces and transfer the crucial decomposition theorems necessary for establishing a wavelet basis from the non-critical values to analogous results for the critical cases now decomposing the reinforced function spaces of Triebel–Lizorkin type.

Critical Shields values in coarse‐bedded steep streams

Critical Shields values ( ) suitable for specific applications are back‐calculated from representative bed load samples in mountain streams and a flow competence/critical flow approach. The general increase of (for the bed D50 size) as well as and (for the bed D16 and D84 sizes) with stream gradient Sx and also the stratification of by relative flow depth and relative roughness are confirmed. Critical Shields values are shown to exceed by about threefold, while those for are nearly half of . However, it remains unclear to what extent physical processes or numerical artifacts contribute to determining critical Shields values. Critical bankfull Shields values ( ) back‐computed from the average largest particles mobile at bankfull flow DBmax,bf approach at steep gradients and at low gradients and therefore increase very steeply with Sx. The relation is stratified by bed stability (D50/DBmax,bf) and predictable if bed stability can be field categorized. Noncritical Shields values ( ) computed from bankfull flow depth and the D50 size differ from and . Only in bankfull mobile streams where D50/DBmax = 1 can τ*cbf, , and be used interchangeably. In highly mobile streams, substituting by overpredicts the DBmax,bf size by up to fivefold and underpredicts DBmax,bf by the same amount in highly stable streams. A value of 0.03 is appropriate for only on low stability beds with Sx ≅ 0.01, but overpredicts DBmax,bf by 30‐fold on highly stable beds with Sx ≅ 0.1. Differences in field and computational methods also affect critical Shields values.

P-adic Eisenstein–Kronecker series and non-critical values of p-adic Hecke L-function of an imaginary quadratic field when the conductor is divisible by p

TextWe relate non-critical special values of p-adic L-functions associated to algebraic Hecke characters of an imaginary quadratic number field with class number one to p-adic Eisenstein–Kronecker series constructed as the Coleman function, when the conductors of the algebraic Hecke characters are divisible by p. VideoFor a video summary of this paper, please click here or visit http://youtu.be/AZemqgfp5pQ.

Spo(2|2) -Equivariant Quantizations on the Supercircle S1|2

We consider the space of differential operators $\mathcal{D}_{\lambda\mu}$ acting between $\lambda$- and $\mu$-densities defined on $S^{1|2}$ endowed with its standard contact structure. This contact structure allows one to define a filtration on $\mathcal{D}_{\lambda\mu}$ which is finer than the classical one, obtained by writting a differential operator in terms of the partial derivatives with respect to the different coordinates. The space $\mathcal{D}_{\lambda\mu}$ and the associated graded space of symbols $\mathcal{S}_{\delta}$ ($\delta=\mu-\lambda$) can be considered as $\mathfrak{spo}(2|2)$-modules, where $\mathfrak{spo}(2|2)$ is the Lie superalgebra of contact projective vector fields on $S^{1|2}$. We show in this paper that there is a unique isomorphism of $\mathfrak{spo}(2|2)$-modules between $\mathcal{S}_{\delta}$ and $\mathcal{D}_{\lambda\mu}$ that preserves the principal symbol (i.e. an $\mathfrak{spo}(2|2)$-equivariant quantization) for some values of $\delta$ called non-critical values. Moreover, we give an explicit formula for this isomorphism, extending in this way the results of [Mellouli N., SIGMA 5 (2009), 111, 11 pages, arXiv:0912.5190] which were established for second-order differential operators. The method used here to build the $\mathfrak{spo}(2|2)$-equivariant quantization is the same as the one used in [Mathonet P., Radoux F., Lett. Math. Phys. 98 (2011), 311-331, arXiv:1003.3320] to prove the existence of a $\mathfrak{pgl}(p+1|q)$-equivariant quantization on $\mathbb{R}^{p|q}$.

Occurrence of POPs in sediments and tissues of European eels (Anguilla anguilla L.) from two Italian lagoons: Varano and Orbetello

1 - Total levels of persistent organic pollutants (polychlorinated biphenyls, organochlorine pesticides, and polycyclic aromatic hydrocarbons) in sediments and edible tissues (muscle and liver) from a fish species of great local commercial interest (Anguilla anguilla L., yellow phase) were determined in Varano and Orbetello lagoons, Italy. 2 - The aim of this study was to improve knowledge on relationships occurring among levels of chemicals in sediments and fish tissues relating them reciprocally and to different intensities of human pressure. 3 - Studied ecosystems were selected due to the notable scientific knowledge acquired by previous detailed research on meteorology, geomorphology, hydrodynamics, types and distribution of local factors linked to different sources of human-made pollution. Samplings were performed in July 2009 according to a logic model based on a priori defined factors of interest and obtained results were statistically analysed in order to evaluate the significance of observed data segregation related to the selected factors. 4 - Concerning levels measured in sediments, significant differences were observed between lagoons in terms of .PAHs and .OCPs. According to National and international recognised sediment quality guidelines, results evidenced the occurrence of non-critical POPs values in sediments. 5 - Results on sediments are associated to very high levels in eel's tissues. Concerning eels, Orbetello lagoon is characterized by significant higher values of .OCPs than Varano, evidencing the presence of an important OCPs local source. 6 - Different human pressure levels produce significant differences in both sediments and eel's tissues in Varano and Orbetello lagoons.

Mock period functions, sesquiharmonic Maass forms, and non-critical values of [formula omitted]-functions

We introduce a new technique of completion for 1-cohomology which parallels the corresponding technique in the theory of mock modular forms. This technique is applied in the context of non-critical values of L-functions of GL(2) cusp forms. We prove that a generating series of non-critical values can be interpreted as a mock period function we define in analogy with period polynomials. Further, we prove that non-critical values can be encoded into a sesquiharmonic Maass form. Finally, we formulate and prove an Eichler–Shimura-type isomorphism for the space of mock period functions.

Incidence and significance of elevated lactate in the identification of critically ill patients

The frequency and characteristics of patients with critical lactate values (>4.0 mmol/L) is unknown. The laboratory database was reviewed for adult patients with non-point of care lactate values over a 6-month period. There were 6914 lactate values, including 625 (9.0%) critical values. Medical records were reviewed in 100 patients with critical and non-critical lactate values. Patients with critical vs. non-critical values had more metabolic acidosis (n=70/100 vs. 22/100, p<0.01), hypotension or tachycardia (n=62/100 vs. 29/100, p<0.01), and a higher 1-month mortality (n=42/100 vs. 7/100, p<0.01). Few patients (n=10/100) with a critical value were not in the emergency department or intensive care unit. Critical lactate values are associated with a longer duration of hospitalization and increased mortality. However, the incremental value of critical lactate values was low, as most patients had abnormal vital signs and laboratory parameters. Requiring notification of lactate values >4.0 mmol/L would be unlikely to augment clinical care.