The translation and transmission of ‘diatribal’ verbs in the textual traditions of the Zlatostruj collection

The ‘diatribe’ is a dialogical mode of exposition, originating in Hellenistic Greek, where the author dramatically performs different voices in a polemical-didactic discourse. The voice of a fictitious opponent is often disambiguated by means of parenthetical verba dicendi, especially φησί(ν). Although diatribal texts were widely translated into Slavic in the Middle Ages, the textual history of the Zlatostruj collection of Chrysostomic homilies especially suits an investigation not only of how Greek ‘diatribal’ verbs were translated, but also how the Slavic verbs were transmitted or developed in different textual traditions. Over time, Slavic redactional activity led to a homogenization of verb forms. The initial variety of the original translation was partly eliminated, and the verb forms "Equation missing" and "Equation missing" became more firmly established as prototypical diatribal formulae. Especially the (increased) use of the 2sg form "Equation missing" has theoretical consequences for the text’s dialogical structure. Thus, an important dialogical component of the diatribe was reinforced in the Zlatostruj’s textual history on Slavic soil.

Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation in almost critical Fourier-Lebesgue spaces

In this paper, we study the one-dimensional cubic nonlinear Schrödinger equation (NLS) on the circle. In particular, we develop a normal form approach to study NLS in almost critical Fourier-Lebesgue spaces. By applying an infinite iteration of normal form reductions introduced by the first author with Z. Guo and S. Kwon (2013), we derive a normal form equation which is equivalent to the renormalized cubic NLS for regular solutions. For rough functions, the normal form equation behaves better than the renormalized cubic NLS, thus providing a further renormalization of the cubic NLS. We then prove that this normal form equation is unconditionally globally well-posed in the Fourier-Lebesgue spaces ℱLp($${\cal F}{L^p}(\mathbb{T})$$ ℱ L p ( T ) ), 1 ≤ p < ∞. By inverting the transformation, we conclude global well-posedness of the renormalized cubic NLS in almost critical Fourier-Lebesgue spaces in a suitable sense. This approach also allows us to prove unconditional uniqueness of the (renormalized) cubic NLS in ℱLp($${\cal F}{L^p}(\mathbb{T})$$ ℱ L p ( T ) ) for $$1 \leq p \leq {3 \over 2}$$ 1 ≤ p ≤ 3 2 .

Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation

We study a chemotaxis-Stokes system with signal consumption and logistic source terms of the form "Equation missing"where $$\kappa \ge 0$$ κ ≥ 0 , $$\mu >0$$ μ > 0 and, in contrast to the commonly investigated variants of chemotaxis-fluid systems, the signal concentration on the boundary of the domain $$\Omega \subset \mathbb {R}^N$$ Ω ⊂ R N with $$N\in \{2,3\}$$ N ∈ { 2 , 3 } is a prescribed time-independent nonnegative function $$c_*\in C^{2}\!\left( {{\,\mathrm{\overline{\Omega }}\,}}\right) $$ c ∗ ∈ C 2 Ω ¯ . Making use of the boundedness information entailed by the quadratic decay term of the first equation, we will show that the system above has at least one global weak solution for any suitably regular triplet of initial data.

Forecasting the Number of the Wounded after an Earthquake Disaster Based on the Continuous Interval Grey Discrete Verhulst Model

Earthquake disaster causes serious casualties, so the prediction of casualties is conducive to the reasonable and efficient allocation of emergency relief materials, which plays a significant role in emergency rescue. In this paper, a continuous interval grey discrete Verhulst model based on kernels and measures (CGDVM-KM), different from the previous forecasting methods, can help us to efficiently predict the number of the wounded in a very short time, that is, an “S-shape” curve for the numbers of the sick and wounded. That is, the continuous interval sequence is converted into the kernel and measure sequences with equal information quantity by the interval whitening method, and it is combined with the classical grey discrete Verhulst model, and then the grey discrete Verhulst models of the kernel and measure sequences are presented, respectively. Finally, CGDVM-KM is developed. It can effectively overcome the systematic errors caused by the discrete form equation for parameter estimation and continuous form equation for simulation and prediction in classical grey Verhulst model, so as to improve the prediction accuracy. At the same time, the rationality and validity of the model are verified by examples. A comparison with other forecasting models shows that the model has higher prediction accuracy and better simulation effect in forecasting the wounded in massive earthquake disasters.

Derivation to Calculate Pipe Collapse Performance using a Combined Loading Equivalent Grade Accounting for Axial Stress, Internal Pressure, Bending and Torsion

This paper proposes a new analytical derivation to incorporate bending and torsion into collapse calculation, further pushing the already existing approach of combined loading equivalent grade proposed in API TR 5C3 (2019) Clause 8.4.6 Eq. (42) for axial stress and internal pressure (identical to ISO TR 10400 Clause 8.4.7) used to calculate a differential collapse pressure. This new derivation is also based on Hencky-von Mises maximum distortion criterion. The interest of developing such combined loading equivalent grade is to enable the use of the four collapse types described in Clause 8 i.e., Yield Strength, Plastic, Transition and Elastic. The formulae are adapted to a closed-form equation similar to current Eq. (42), enabling pipe collapse performance calculation. Newly derived formulae are checked against a size governed by yield strength collapse to verify consistency. The restrictions regarding collapse performance under compression are discussed.

How Large Are Firing Costs? A Cross-Country Study

This paper provides evidence for the size and the cyclicality of firing costs for the United States and Germany. In contrast to the existing literature, we use the optimality conditions obtained in a search and matching model to find a reduced form equation for firing costs. We find that our estimates are slightly larger compared with other studies and document sizable time-variation in firing costs.

Positive Rational Number of the Form (Equation)

Let (Equation) and (Equation) be positive integers with (Equation) . In this paper, we show that every positive rational number can be written as the form (Equation) , where m,n∈N if and only if (Equation) or (Equation) . Moreover, if (Equation) , then the proper representation of such representation is unique.

FE SOLUTIONS OF NEAR-TIP FIELD FOR MODE-I CRACKS WITH RESIDUAL SURFACE TENSION

This paper presents finite element solutions of a near-tip elastic field of a straight, nano-scale crack in a two-dimensional, linear elastic, whole plane subjected to mode-I crack-face loads. The mathematical model is formulated using a continuum-based theory of classical linear elasticity together with Gurtin-Murdoch surface model to capture the role of the residual surface tension present on the crack-face material layer. The formulation finally yields a second-order, integrodifferential equation governing the crack opening displacement. A weighted residual technique along with the regularization procedure is applied to establish a weakly singular weak-form equation with the involved kernel of O(ln )r . Galerkin strategy and the finite element procedure are then employed to discretize the weak-form equation. Various types of element shape functions, generated by standard C0 -elements, standard C1 -elements, and special elements with built-in crack-tip functions, are considered. A proper quadrature rule is selected to efficiently and accurately evaluate both nearly and weakly singular double line integrals over pairs of elements resulting from the discretization and the solution of a dense system of linear algebraic equations is obtained using an efficient indirect solver. The rate of convergence of finite element solutions is fully investigated and such information is then used to conclude the influence of the residual surface tension on the behavior of the near-tip field.