Impulsive simulation model for the dynamics of allergen immunotherapy

This study aims to analyze the effects of allergen immunotherapy, used to treat allergic symptoms such as pollen allergy. Mathematical models are used as a methodological approach to simulate from a system of impulsive differential equations the dynamics of the model. Immunotherapy is based of supplying small amounts of pollen to the patient, which leads to minimizing severe allergic symptoms when patients are subsequently exposed to higher amounts of pollen in the environment. Lymphocyte concentrations are considered state variables, allowing the behavior and efficacy of allergen immunotherapy to be identified. The manuscript proposes a method that allows to model mixed systems. Phenomena that present continuous times in some instants and discrete times in others, these are phenomena that are frequently found in the field of physics. Allergen immunotherapy is most effective when a treatment is created with pollen dose increments in a linear form.

The norming set of a symmetric 3-linear form on the plane with the $l_1$-norm

An element $(x_1, \ldots, x_n)\in E^n$ is called a {\em norming point} of $T\in {\mathcal L}(^n E)$ if $\|x_1\|=\cdots=\|x_n\|=1$ and$|T(x_1, \ldots, x_n)|=\|T\|,$ where ${\mathcal L}(^n E)$ denotes the space of all continuous $n$-linear forms on $E.$For $T\in {\mathcal L}(^n E),$ we define $${Norm}(T)=\Big\{(x_1, \ldots, x_n)\in E^n: (x_1, \ldots, x_n)~\mbox{is a norming point of}~T\Big\}.$$${Norm}(T)$ is called the {\em norming set} of $T$. We classify ${Norm}(T)$ for every $T\in {\mathcal L}_s(^3 l_{1}^2)$.

Universe as Klein–Gordon eigenstates

We formulate Friedmann’s equations as second-order linear differential equations. This is done using techniques related to the Schwarzian derivative that selects the$$\beta $$ β -times $$t_\beta :=\int ^t a^{-2\beta }$$ t β : = ∫ t a - 2 β , where a is the scale factor. In particular, it turns out that Friedmann’s equations are equivalent to the eigenvalue problems $$\begin{aligned} O_{1/2} \Psi =\frac{\Lambda }{12}\Psi , \quad O_1 a =-\frac{\Lambda }{3} a , \end{aligned}$$ O 1 / 2 Ψ = Λ 12 Ψ , O 1 a = - Λ 3 a , which is suggestive of a measurement problem. $$O_{\beta }(\rho ,p)$$ O β ( ρ , p ) are space-independent Klein–Gordon operators, depending only on energy density and pressure, and related to the Klein–Gordon Hamilton–Jacobi equations. The $$O_\beta $$ O β ’s are also independent of the spatial curvature, labeled by k, and absorbed in $$\begin{aligned} \Psi =\sqrt{a} e^{\frac{i}{2}\sqrt{k}\eta } . \end{aligned}$$ Ψ = a e i 2 k η . The above pair of equations is the unique possible linear form of Friedmann’s equations unless $$k=0$$ k = 0 , in which case there are infinitely many pairs of linear equations. Such a uniqueness just selects the conformal time $$\eta \equiv t_{1/2}$$ η ≡ t 1 / 2 among the $$t_\beta $$ t β ’s, which is the key to absorb the curvature term. An immediate consequence of the linear form is that it reveals a new symmetry of Friedmann’s equations in flat space.

Preferential Attachment and Fitness in the Evolution of the Brazilian Film Network

This study analyzes the network evolution, specifically that of the Brazilian film network. It examines two generative mechanisms that lie behind the network evolution: preferential attachment and fitness. The starting point is that preferential attachment and fitness may compete to shape the network evolution. We built a novel dataset with 974 Brazilian feature films released between 1995 and 2017 and used PAFit, a brand-new statistical method, to estimate the joint effects of preferential attachment and fitness on the evolution of the Brazilian film network. This study concludes that the network evolution is shaped by both preferential attachment and fitness. However, in the presence of fitness, the effects of preferential attachment on the network evolution become weaker. This means that the node ability to form ties in the Brazilian film network is mainly explained by its fitness. Besides, the preferential attachment assumes a sub-linear form. Costs, communication and managerial capabilities, and node age explain why nodes are unable to accumulate ties at rates proportional to their degree. Finally, preferential attachment and fitness manifest themselves heterogeneously, depending on either the type or the duration of the network. Preferential attachment drives the cast network evolution, whereas fitness is the main generative mechanism of the crew network. Actors and actresses rely on their status, privilege, and power to obtain future contracts (preferential attachment), whereas technical members are selected on the basis of their talent, skills, and knowledge (fitness). Due to node age or exit, preferential attachment becomes stronger in shorter networks.

Ligação Preferencial e Aptidão na Evolução da Rede de Filmes Brasileiros

This study analyzes the network evolution, specifically that of the Brazilian film network. It examines two generative mechanisms that lie behind the network evolution: preferential attachment and fitness. The starting point is that preferential attachment and fitness may compete to shape the network evolution. We built a novel dataset with 974 Brazilian feature films released between 1995 and 2017 and used PAFit, a brand-new statistical method, to estimate the joint effects of preferential attachment and fitness on the evolution of the Brazilian film network. This study concludes that the network evolution is shaped by both preferential attachment and fitness. However, in the presence of fitness, the effects of preferential attachment on the network evolution become weaker. This means that the node ability to form ties in the Brazilian film network is mainly explained by its fitness. Besides, the preferential attachment assumes a sub-linear form. Costs, communication and managerial capabilities, and node age explain why nodes are unable to accumulate ties at rates proportional to their degree. Finally, preferential attachment and fitness manifest themselves heterogeneously, depending on either the type or the duration of the network. Preferential attachment drives the cast network evolution, whereas fitness is the main generative mechanism of the crew network. Actors and actresses rely on their status, privilege, and power to obtain future contracts (preferential attachment), whereas technical members are selected on the basis of their talent, skills, and knowledge (fitness). Due to node age or exit, preferential attachment becomes stronger in shorter networks.

Concept Map Assessment: An Experimental Mathematical Study

In this experimental study, we analyzed the ability to understand and ability to share mathematical knowledge of our modified context maps (MCM) and compared them to the standard linear form of examination. For these purposes, the categorization of mathematical knowledge to local and structural understanding and craft was defined. Experimentation was conducted during the regular final oral exam of Linear algebra courses for computer science freshmen university students. No benefits were given for participation in the experiment.According to the questionnaire self-report student data, the MCM method combined with student-examiner discussion shares statistically significantly better structural understanding than the linear form. However, the MCM method shares less local understanding than the linear form, given randomized data set. Moreover, students claim that the MCM oral examination form is almost as objective as other oral exams they attempted during faculty study. Students created surprisingly good modified cognitive maps, although we assumed their low to none practical experience with concept mapping.

Ca2+ removal from water by the use of Na-palygorskite for potential water softening

Sodium-treated palygorskite (Na-Pal) sample was investigated for the sorption of Ca2+ ions with the aim of treating water hardness. The effective modification of the mineral with Na+ was verified by XRD and FT-IR techniques. Batch kinetic experiments in standard solutions were performed proving that 30 g/L of Na-Pal were highly satisfactory as the Ca2+ removal reached the 85% for 100 mg/L Ca2+ initial concentration, which is very promising for the softening of moderate or hard waters. The Ca2+ removal found to be pH and temperature independent, with high removal rates at room temperature and common pH values of water samples (pH 4–12), rendering these circumstances ideal for the low-cost maintenance of the procedure that took place within the first 5 min. The linear form of the Langmuir isotherm model expressed better (R2 = 1) the Ca2+ sorption, which means that takes place at specific homogeneous sites of Na-Pal. Thermodynamic analysis proved the non-spontaneous (positive ΔG0), physical, and exothermic nature (ΔH0 = −10.8197 kJ/mol) of the reaction, while the kinetic models proved the chemisorption of Ca2+ by Na-Pal.

Possibilities of skin ultrasound examination in the management of patients with localized scleroderma

With the help of ultrasound examination (ultrasound), it is possible to visualize the skin of patients with suspected localized scleroderma, as well as to objectively determine the stage of the disease and assess the effectiveness of therapy. Three patients with linear, plaque forms of scleroderma, as well as lichen sclerosus, underwent skin ultrasound using a Skinscanner DUB TPM device with a 75 MHz transducer, 4 mm penetration, 21 m resolution in the area of lesions and in adjacent areas of healthy skin, using their ratio coefficient (RC) for comparative evaluation. The thickness of the epidermis and dermis, their echogenicity were determined. With a linear form of scleroderma, an increase in the thickness of the epidermis in the area of the focus (RC 0.850.0125) and a decrease in its echogenicity (RC 1.580.46) were observed. The echogenicity of the dermis was significantly reduced in the lesion (RC 3.021.17). The dermis thickness was slightly less in the center of the lesion (RC 1.09), at the periphery of the lesion it was moderately increased (RC 0.86). In the plaque form of scleroderma, a decrease in the echogenicity of the epidermis was observed in the foci (RC 1.320.49); an increase in the thickness of the dermis (RC 0.790.16) and a decrease in its e echogenicity (RC 1.260.57). In 7 of 11 foci, a subepidermal hypoechoic band was visualized. With lichen sclerosis in the foci, an increase in the thickness of the epidermis (RC 0.420.12) and its acoustic density (RC 0.630.0793), a decrease in the thickness and echo density of the dermis (RC 1.320.00943 and RC 1.550.6, respectively). With different forms of LS, a different ultrasound picture was observed, depending on the stage and activity of the process. The changes identified during treatment reflect the effectiveness of the therapy and the rate of restoration of the skin structure during therapy.

Kinetic equation having the integral scattering term with a linear form of external electrical and magnetic fields

In many cases, nobody consider any kinetic equation where the collision integral does not use clearly the values of external electric and magnetic fields. But there is some reason to use in the collision integral the above fields and to consider the ratio of the averaged deBroglie wavelength to the free-path length.