C1 Function Research Articles

Outgoing modal solutions for Galbrun's equation in helioseismology

We construct modal outgoing Green's kernels for the simplified Galbrun's equation under spherical symmetry, in the context of helioseismology. The coefficients of the equation are C2 functions representing the solar interior model S, complemented with an isothermal atmospheric model. We solve the equation in vectorial spherical harmonics basis to obtain modal equations for the different components of the unknown wave motions. These equations are then decoupled and written in Schrödinger form, whose coefficients are shown to be C2 apart from at most two regular singular points, and to decay like a Coulomb potential at infinity. These properties allow us to construct an outgoing Green's kernel for each spherical mode. We also compute asymptotic expansions of coefficients up to order r−3 as r tends to infinity, and show numerically that their accuracy is improved by including the contribution from the gravity although this term is of order r−3.

A Weyl pseudodifferential calculus associated with exponential weights on Rd

We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted Lp spaces over Rd with weights of the form exp(−ϕ(x)), for ϕ a C2 function, a setting in which the operator associated to the weighted Dirichlet form typically has only holomorphic functional calculus. A symbol class giving rise to bounded operators on Lp is determined, and its properties are analyzed. This theory is used to calculate an upper bounded on the H∞ angle of relevant operators and deduces known optimal results in some cases. Finally, the symbol class is enriched and studied under an algebraic viewpoint.

Angioedema without wheals: a clinical update

Angioedema without wheals (urticaria) represents a heterogeneous group of clinically indistinguishable diseases of hereditary or acquired etiology. Hereditary angioedema is a rare inherited condition leading to recurrent, sometimes life-threatening angioedema attacks in subcutaneous tissues and gastrointestinal and oropharyngeal mucosa dating back to childhood or adolescence. Most of these patients have mutations in the SERPING1 gene, causing either low C1 inhibitor production (hereditary angioedema with C1 inhibitor deficiency type I) or the production of dysfunctional C1 inhibitor (hereditary angioedema with C1 inhibitor deficiency type II). Hereditary angioedema with normal C1 inhibitor has been defined later. Although C1 inhibitor concentration and function are in the normal range, it leads to typical hereditary angioedema symptoms owing to mutations in FXII, PLG, ANGPT1, KNG1, and MYOF genes. Patients who exhibit none of these genetic mutations despite having a similar clinical presentation are classified as having unknown hereditary angioedema. Fewer than 1 in 10 patients with C1 inhibitor deficiency have acquired angioedema with C1 inhibitor deficiency. The clinical presentation is very similar to that of hereditary angioedema, making it difficult to distinguish these 2 conditions clinically. Unlike hereditary angioedema, there are no genetic mutations, and family history and symptoms tend to appear later in life. Acquired angioedema with C1 inhibitor deficiency is commonly associated with lymphoproliferative and autoimmune diseases. Angioedema attacks might start 1 year before the underlying disease in acquired angioedema with C1 inhibitor deficiency. Approximately half of the patients admitted to the hospital for acute angioedema are patients receiving angiotensin-converting enzyme (ACE) inhibitor therapy. Angioedema typically occurs on the lips, tongue, mouth, pharynx, and subglottic regions. Patients may require hospitalization and intensive care monitoring owing to airway involvement. Idiopathic histaminergic acquired angioedema may be diagnosed only when any possible causes of histaminergic angioedema are excluded (foods, drugs, animal dander, aeroallergens, insect stings, latex, and others), and the symptoms respond well to antihistamine treatment. Idiopathic nonhistaminergic acquired angioedema should be considered when all other types of recurrent angioedema have been ruled out and patients do not respond to high-dose antihistamines. The lack of a standard biochemical laboratory test for patients with idiopathic histaminergic acquired angioedema, idiopathic nonhistaminergic acquired angioedema, angiotensin-converting enzyme inhibitor-induced acquired angioedema, and hereditary angioedema with normal C1 inhibitor makes the diagnosis more challenging. Future efforts should focus on increasing awareness of all the rare types of angioedema among physicians and developing more straightforward and more accessible diagnostic methods.

Periodic Severe Angioedema without Exogenous Hormone Exposure

Hereditary angioedema (HAE) is characterized by recurrent attacks of skin and mucosal swelling in any part of the body including the digestive and respiratory tract which generally improve spontaneously within 12-72 hours. The underlying mechanism in HAE is related to bradykinin dysregulation which causes these attacks not to respond to common treatment strategies including epinephrine/corticosteroid or adrenaline. There are several types of HAE with different etiology but with the same clinical picture. Type 1 is due to the deficiency of C1 Inhibitor (C1-INH) protein and type 2 is related to dysfunctional C1-INH protein. The third type of HAE which comprises the minority of cases is associated with the normal amount and function of C1-INH protein. The presented case in this report was a 15-years old girl with a history of spontaneous angioedema attacks from the age of 14. The frequency of attacks was initially every two months but consequently increased to every two weeks after using some hormonal medications for ovarian cyst. Each episode has lasted around 10 days without any symptoms in between. Complement studies including C4, C1q, and C1-INH protein, both quantitative and qualitative, were reported as normal. A genetic assessment revealed a mutation in the exon 9 on the gene related to factor XII, hence the diagnosis of HAE type 3 was confirmed. This was a rare type of angioedema with normal amount and function of C1-INH protein which is predominantly seen in women during periods of imbalanced estrogen increments like pregnancy, lactation, and menopause, and hence it is responsive to hormonal manipulation strategies such as the use of progesterone containing medications.

Linear Lipschitz and C1 extension operators through random projection

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C1 extension theorem by Whitney [8] to Banach spaces.

English

We construct some nondecreasing quantities associated to the first eigenvalue of $$ - {{\rm{\Delta }}_\varphi } + cR\left( {c \ge {1 \over 2}\left( {n - 2} \right)/\left( {n - 1} \right)} \right)$$ along the Yamabe flow, where Δφ is the Witten-Laplacian operator with a C2 function φ. We also prove a monotonic result on the first eigenvalue of $$ - {{\rm{\Delta }}_\varphi } + {1 \over 4}\left( {n/\left( {n - 1} \right)} \right)R$$ along the Yamabe flow. Moreover, we establish some nondecreasing quantities for the first eigenvalue of −Δφ + cRa with a ∈ (0,1) along the Yamabe flow.

Structural, optical and junction characteristics of pyrazolo pyridine derivatives

Two pyridine derivatives, 6-(2-chlorophenyl)-2,3-dihydro-1-methyl-3-oxo-2-phenyl-1H-pyrazolo[4,3-b]pyridine-5-carbonitrile (C1) and 6-(4-chlorophenyl)-2,3-dihydro-1-methyl-3-oxo-2-phenyl-1H-pyrazolo[4,3-b] pyridine-5-carbonitrile (C2) are prepared and characterized. Different techniques were applied to confirm their molecular structures. The thermal, structural, optical and diode characteristics of the two pyridine derivatives are reported. X-ray diffraction (XRD) patterns of C1 and C2 in powder form reveal monoclinic polycrystalline nature. The optical functions of C1 and C2 films are calculated from the transmittance and reflectance spectra measured over the spectral range 200–2500 nm. Two indirect allowed optical energy gaps were estimated; 2.55 and 3.13 eV for C1 and 2.7 and 3.27 eV for C2. Thin films of the two compounds were deposited onto p-Si substrates for fabricating heterojunctions. The diode ideality factor and barrier height of both devices were calculated. In addition, Norde's function was used to determine the important parameters of the devices. At relatively high voltage, the conduction mechanism is described by space charge limited current in both devices. The conduction of the device based on C1 and C2 compounds are due to pool–Frenkel and Schottky mechanisms. The data at reverse biasing are also analyzed and estimated. The device based on C1 compound did not give any response to light, while that based on C2 can used as photosensor.

Strategic Diastereoselective C1 Functionalization in the Aza-Rocaglamide Scaffold toward Natural Product-Inspired eIF4A Inhibitors.

Rocaglates, rocaglamides, and related flavagline natural products exert their remarkable anticancer activity through inhibition of eukaryotic initiation factor 4A (eIF4A) but generally display suboptimal drug-like properties. In our efforts to identify potent drug-like eIF4A inhibitors, we developed synthetic strategies for diastereoselectively functionalizing the C1 position of aza-rocaglamide scaffolds (cf. 14 and 18), which proceed via retention or inversion of configuration at C1 depending on the C2 substituent (cf. 15 and 21) and ultimately enabled the discovery of novel and potent eIF4A inhibitors such as 25.

Febuxostat inhibited axillary osmidrosis risk factor ATP-binding cassette transporter C11 in vitro.

The authors have a patent pending related to the work reported in this article. Appendix S1. Supplementary Methods. Figure S1. Febuxostat hardly affected ATP-binding cassette transporter C2 (ABCC2) function. Table S1. Key resources. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Idiopathic nonhistaminergic acquired angioedema in a patient with coronavirus disease 2019

Idiopathic nonhistaminergic acquired angioedema in a patient with coronavirus disease 2019

Perturbations of local maxima and comparison principles for boundary-degenerate linear differential equations

We develop strong and weak maximum principles for boundary-degenerate elliptic and parabolic linear second-order partial differential operators, A u := − t r ( a D 2 u ) − ⟨ b , D u ⟩ + c u Au := -\mathrm {tr}(aD^2u)-\langle b, Du\rangle + cu , with partial Dirichlet boundary conditions. The coefficient, a ( x ) a(x) , is assumed to vanish along a nonempty open subset, ∂ 0 O \partial _0\mathscr {O} , called the degenerate boundary portion, of the boundary, ∂ O \partial \mathscr {O} , of the domain O ⊂ R d \mathscr {O}\subset \mathbb {R}^d , while a ( x ) a(x) is nonzero at any point of the nondegenerate boundary portion, ∂ 1 O := ∂ O ∖ ∂ 0 O ¯ \partial _1\mathscr {O} := \partial \mathscr {O}\setminus \overline {\partial _0\mathscr {O}} . If an A A -subharmonic function, u u in C 2 ( O ) C^2(\mathscr {O}) or W l o c 2 , d ( O ) W^{2,d}_{\mathrm {loc}}(\mathscr {O}) , is C 1 C^1 up to ∂ 0 O \partial _0\mathscr {O} and has a strict local maximum at a point in ∂ 0 O \partial _0\mathscr {O} , we show that u u can be perturbed, by the addition of a suitable function w ∈ C 2 ( O ) ∩ C 1 ( R d ) w\in C^2(\mathscr {O})\cap C^1(\mathbb {R}^d) , to a strictly A A -subharmonic function v = u + w v=u+w having a local maximum in the interior of O \mathscr {O} . Consequently, we obtain strong and weak maximum principles for A A -subharmonic functions in C 2 ( O ) C^2(\mathscr {O}) and W l o c 2 , d ( O ) W^{2,d}_{\mathrm {loc}}(\mathscr {O}) which are C 1 C^1 up to ∂ 0 O \partial _0\mathscr {O} . Points in ∂ 0 O \partial _0\mathscr {O} play the same role as those in the interior of the domain, O \mathscr {O} , and only the nondegenerate boundary portion, ∂ 1 O \partial _1\mathscr {O} , is required for boundary comparisons. Moreover, we obtain a comparison principle for a solution and supersolution in W l o c 2 , d ( O ) W^{2,d}_{\mathrm {loc}}(\mathscr {O}) to a unilateral obstacle problem defined by A A , again where only the nondegenerate boundary portion, ∂ 1 O \partial _1\mathscr {O} , is required for boundary comparisons. Our results extend those of Daskalopoulos and Hamilton, Epstein and Mazzeo, and Feehan, where t r ( a D 2 u ) \mathrm {tr}(aD^2u) is in addition assumed to be continuous up to and vanish along ∂ 0 O \partial _0\mathscr {O} in order to yield comparable maximum principles for A A -subharmonic functions in C 2 ( O ) C^2(\mathscr {O}) , while the results developed here for A A -subharmonic functions in W l o c 2 , d ( O ) W^{2,d}_{\mathrm {loc}}(\mathscr {O}) are entirely new. Finally, we obtain analogues of all the preceding results for parabolic linear second-order partial differential operators, L u := − u t − t r ( a D 2 u ) − ⟨ b , D u ⟩ + c u Lu := -u_t - \mathrm {tr}(aD^2u)-\langle b, Du\rangle + cu .

Particle number balance approach for simulation of a multi-chamber fluidized bed urea granulator; Modeling and validation

In the present work, a model was proposed to simulate the growth in an industrial multi-chamber fluidized bed granulator under steady-state condition. To simulate the growth, it was assumed the coating is the only growth mechanism. Mass balance, as well as particle number balance (PNB), was considered in the simulation. Despite previous works, it was not assumed that particles in each chamber are at the same age. Consequently, the growth was simulated along the granulator length, from its beginning to the end. In this model, most of the influencing parameters are collected in one parameter called C1. Using finite difference method, equations were solved and results were compared with samples from an industrial granulator and very good agreements were observed. Sensitivity of the product normalized mass density function to the parameter C1 was also studied. It was found that for a specific inlet seeds diameter distribution, d50 of the product is not a linear function of C1.

Exploring Potential Correlation Between CEFR Grammar Profile in English and Learners’ Overall Grammar Knowledge: An Exploratory Study of “that”

This preliminary study explored the possibility of using an opaque polysemous grammatical unit as a representation for the whole grammatical knowledge of a learner. There were two groups of informants, a group with a certified language proficiency level at CEFR B1-B2 and a learner group at A1-A2 level. The informants were asked to provide a Thai translation of an English text as faithful as possible. The first group consistently and correctly answered the questions by supplying the right translation of polysemous “that” while the answers from the second group were divided in that some could correctly identify C2 function of the word, “that”, though their overall grammatical knowledge was considered to be at A1 but other A2 students failed to identify C2 function of the word in question. The result indicated that the grammatical construction in question could not be used as a key predictor for learners’ syntactic representation as the lineage relation between CEFR level of the grammatical unit corresponded with the translated texts provided to a limited extent. On pedagogical implications, insights provided suggested that instructors should spend more time explaining challenging advanced grammatical functions as they were points that learners were struggling with and one possible way to check whether they did understand syntactic meaning of a function word was by asking students to supply a translation.

Existence and multiplicity results for some Schrödinger-Poisson system with critical growth

In this paper we study the existence and multiplicity of positive solutions for the Schrödinger-Poisson system with critical growth:{−ε2Δu+V(x)u=f(u)+|u|3uϕ,x∈R3,−ε2Δϕ=|u|5,x∈R3,u∈H1(R3),u(x)>0,x∈R3, where ε>0 is a parameter, V:R3→R is a continuous function and f:R→R is a C1 function. Under a global condition for V we prove that the above problem has a ground state solution and relate the number of positive solutions with the topology of the set where V attains its minimum, by using variational methods.

The Unfolded Protein Response Modulates a Phosphoinositide-Binding Protein through the IRE1-bZIP60 Pathway.

Phosphoinositides function as lipid signals in plant development and stress tolerance by binding with partner proteins. We previously reported that Arabidopsis (Arabidopsis thaliana) phosphoinositide-specific phospholipase C2 functions in the endoplasmic reticulum (ER) stress response. However, the underlying molecular mechanisms of how phosphoinositides act in the ER stress response remain elusive. Here, we report that a phosphoinositide-binding protein, SMALLER TRICHOMES WITH VARIABLE BRANCHES (SVB), is involved in the ER stress tolerance. SVB contains a DUF538 domain with unknown function; orthologs are exclusively found in Viridiplantae. We established that SVB is ubiquitously expressed in plant tissues and is localized to the ER, Golgi apparatus, prevacuolar compartment, and plasma membrane. The knockout mutants of svb showed enhanced tolerance to ER stress, which was genetically complemented by transducing genomic SVB SVB showed time-dependent induction after tunicamycin-induced ER stress, which depended on IRE1 and bZIP60 but not bZIP17 and bZIP28 in the unfolded protein response (UPR). A protein-lipid overlay assay showed specific binding of SVB to phosphatidylinositol 3,5-bisphosphate and phosphatidylinositol 3,4,5-trisphosphate. SVB is therefore suggested to be the plant-specific phosphoinositide-binding protein whose expression is controlled by the UPR through the IRE1-bZIP60 pathway in Arabidopsis.

On a lattice-like property of quasi-arithmetic means

We will prove that every pair of quasi-arithmetic means satisfying certain smoothness assumption has the supremum and the infimum in this set. More precisely, if f and g are C2 functions with nowhere vanishing first derivative then there exists a function h such that: (i) A[f]≤A[h], (ii) A[g]≤A[h], and (iii) for every continuous strictly monotone function s:I→RA[f]≤A[s]andA[g]≤A[s]impliesA[h]≤A[s] (A[f] stands for a quasi-arithmetic mean). Moreover, h∈C2, h′≠0, and it is a solution of the differential equationh″h′=max⁡(f″f′,g″g′). We also provide some extension to a finite family of means and dual (reflected) result.

On an optimal quadrature formula for approximation of Fourier integrals in the space [formula omitted

This paper deals with the construction of an optimal quadrature formula for approximation of Fourier integrals in the Sobolev space L2(1)[a,b] of non-periodic, complex valued functions which are square integrable with first order derivative. Here the quadrature sum consists of linear combination of the given function values in a uniform grid. The difference between the integral and the quadrature sum is estimated by the norm of the error functional. The optimal quadrature formula is obtained by minimizing the norm of the error functional with respect to coefficients. Analytic formulas for optimal coefficients can also be obtained using discrete analogue of the differential operator d2∕dx2. In addition, the convergence order of the optimal quadrature formula is studied. It is proved that the obtained formula is exact for all linear polynomials. Thus, it is shown that the convergence order of the optimal quadrature formula for functions of the space C2[a,b] is O(h2). Moreover, several numerical results are presented and the obtained optimal quadrature formula is applied to reconstruct the X-ray Computed Tomography image by approximating Fourier transforms.

Work output and thermal efficiency of an endoreversible entangled quantum Stirling engine with one dimensional isotropic Heisenberg model

The heat engine with entangled quantum system as working medium is called quantum entanglement heat engine A model of an endoreversible entangled quantum Stirling engine with heat transfer loss in which a one dimensional isotropic Heisenberg model is used as working medium is established in this paper. The thermodynamic performance of the endoreversible entangled quantum Stirling engine is studied by using the combination of quantum thermodynamics and finite time thermodynamics. Explicit expressions of dimensionless work output and thermal efficiency of the endoreversible entangled quantum Stirling engine are derived. Two linearly independent concurrences c1 and c3 are considered as a measure of entanglement of a two-qubits state. They are employed to study the influence of entanglement on the performance of the endoreversible entangled quantum Stirling engine. It is found that both the dimensionless work output and thermal efficiency are dependent on c1 and c3. Scince c1 and c3 are functions of temperature (T) and magnetic-field (B), it is possible to apply quantum control on the work output of the endoreversible entangled quantum Stirling engine by adjusting the values of T and B. There exists an optimal concurrence c1 which leads to a maximum work output W∗. While W∗ increases with increase of c3. The thermal efficiency η is a monotonically increasing function of c1 and c3. The maximum dimensionless work outputs corresponding to c3=0.7, c3=0.725 and c3=0.75 are 0.16255, 0.18965 and 0.21764, respectively. The corresponding thermal efficiencies are 0.3482, 0.37804 and 0.40637, respectively.

Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part II: Generic nonlinearities

We consider the Cauchy problem where f is a C1 function on with and u0 is a nonnegative continuous function on whose limits at are equal to 0. Assuming that the solution u is bounded, we study its asymptotic behavior as In the first part of this study, we proved a general quasiconvergence result: as the solution approaches a set of steady states in the topology of In this paper, we show that under certain generic, explicitly formulated conditions on the nonlinearity f, the solution necessarily converges to a single steady state in Then, under the same conditions, we describe the global asymptotic shape of the solution: the graph of has a top part close to the graph of and two sides taking shapes of “terraces” moving in the opposite directions with precisely determined speeds.

Investigation of the influence of supercritical carbon dioxide treatment on meta-aramid fiber: Thermal decomposition behavior and kinetics

Influence of supercritical carbon dioxide (SCF-CO2) on the thermal decomposition behavior and kinetics of meta-aramid fiber was investigated at the first time, in order to develop some fundamental bases for sustainably and cleanly manufacturing some relative products from this fiber with the supercritical green medium. Particularly, the thermal decomposition behavior of treated samples was explored and characterized by thermogravimetric and differential thermogravimetric analysis (TGA-DTGA). The kinetics of the main steps of thermal decomposition was also investigated via different kinetics models. The results show that an influence of SCF-CO2 treatment on the thermal decomposition behavior of the fiber was observed by TGA-DTGA, accompanied with successive and partially overlapped predominant two-step degradation as sample temperature from 380.0 °C to 700.0 °C, as well as a small pyrolysis Step three at 650.0 °C to 800.0 °C. Decreases in thermal property and behavior were detected by TGA-DTGA for the samples as treatment temperature from 80.0 °C to 120.0 °C. The fitted results reveal that good linear regressions of the TGA-DTGA data were achieved from the kinetics models accompanied with high values of adjusted R-Square. The kinetics parameter of the apparent activation energy (E) decreased with the treatment temperature from 80.0 °C to 120.0 °C, as well as with the conversion degree (α) of the samples. Moreover, a second-order chemical reaction mechanism for the predominant thermal decomposition steps was successfully supposed by Coats-Redfern and Achar-Brindley-Sharp-Wendworth models combined with a solid mechanism function of C2.