Yang-Baxter and the Boost: splitting the difference

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

Differences over Difference: Sino-Russian Friendship at Interstate and Interpersonal Scales

Relations between states are usually framed in human terms, from partners to rivals, enemies or allies, polities and persons appear to engage in cognate relationships. Yet whether or not official ties and relationships among people from those states actually correspond remains less clear. “Friendship,” a term first applied to states in eighteenth-century Europe and mobilized in the (post)socialist world since the 1930s, articulates with particular clarity both the promise and the limitations of harmonized personal and state ties. Understandings of friendship vary interculturally, and invocations of state-state friendship may be accompanied by a distinct lack of amity among populations. Such is the case between China and Russia today, and this situation therefore raises wider questions over how we should understand interstate and interpersonal relationships together. Existing social scientific work has generally failed to locate either the everyday in the international or the international in the everyday. Focusing on both Chinese and Russian approaches to daily interactions in a border town and the official Sino-Russian Friendship, I thus suggest a new scalar approach. Applying this to the Sino-Russian case in turn reveals how specific contours of “difference” form a pivot around which relationships at both scales operate. This study thus offers both comparison between Chinese and Russian friendships, and a lens for wider comparative work in a global era of shifting geopolitics and cross-border encounters.

Mathematical modeling of filling the CCM mold with liquid metal during its supply from a rotating submersible nozzle

Experimental studies of the flow of liquid metal in CCM mold are long, complex and labor consuming process. Therefore, mathematical modeling by numerical methods is increasingly used for this purpose. The article considers a new technology for liquid metal supply into a mold. The authors present original patented design of the device, consisting of direct-flow and rotating bottom nozzles. The main results of investigations of the melt flow in the mold are considered. The objects of research were hydrodynamic and heat flows of liquid metal at new process of steel casting into a CCM mold of rectangular section. The result is spatial mathematical model describing flows and temperatures of liquid metal in the mold. To simulate the processes occurring during metal flow in the mold, special software was designed. Theoretical calculations are based on fundamental equations of hydrodynamics, equations of mathematical physics (equation of heat conduction taking into account mass transfer) and proven numerical method. The area under study was divided into elements of finite dimensions; for each element, resulting system of equations was written in difference form. The results are fields of velocities and temperatures of metal flow in the mold volume. A calculation program was compiled based on developed numerical schemes and algorithms. An example of calculation of steel casting into a mold of rectangular cross-section, and flow diagrams of liquid metal along various sections of the mold are given. Vector flows of liquid metal in different sections of the mold are clearly presented at different angles of rotation of the deep-bottom nozzle. The authors have identified the areas of intense turbulence. Metal flows of the described technological process were compared with traditional metal supply through a fixed bottom nozzle.

THE SLICE BALANCE APPROACH USING AN ADAPTIVE-WEIGHTED CLOSURE

In this paper, we present a formulation of the slice balance approach using a nonlinear closure relation derived analogously from the adaptive-weighted diamond-difference form of the weighted diamond-difference method for Cartesian grids. The method yields strictly positive solutions that reduce to a standard diamond closure with fine-enough mesh granularity. It can be efficiently solved using Newton-like nonlinear iterative methods with diffusion preconditioning.

Impact of Economic Growth, Financial Development, and Trade Openness on Environmental Degradation in Egypt

This paper examines the effects of economic growth, financial development, and trade openness on the environment quality measured by CO2 emissions over the period of 1965–2014 in the case of Egypt. In this study, the series were stationary at their first difference form, and thus, a long-run model was adopted using the vector error correction model technique. The results confirm that the variables are cointegrated, indicating the long-run relationship between the variables. The empirical findings reveal a negative influence of economic growth and financial effect of the previous period of CO2 emissions, these effects are not significant in the short run. Any deviations from the long-run equilibrium return quickly, representing 59% speed of adjustment. The study proposes new policy insights into reduce CO2 emissions, especially in the long run.

On the discrete version of the black hole solution

A Schwarzschild-type solution in Regge calculus is considered. Earlier, we considered a mechanism of loose fixing of edge lengths due to the functional integral measure arising from integration over connection in the functional integral for the connection representation of the Regge action. The length scale depends on a free dimensionless parameter that determines the final functional measure. For this parameter and the length scale large in Planck units, the resulting effective action is close to the Regge action. Earlier, we considered the Regge action in terms of affine connection matrices as functions of the metric inside the 4-simplices and found that it is a finite-difference form of the Hilbert–Einstein action in the leading order over metric variations between the 4-simplices. Now we take the (continuum) Schwarzschild problem in the form where spherical symmetry is not set a priori and arises just in the solution, take the finite-difference form of the corresponding equations and get the metric (in fact, in the Lemaitre or Painlevé–Gullstrand like frame), which is nonsingular at the origin, just as the Newtonian gravitational potential, obeying the difference Poisson equation with a point source, is cutoff at the elementary length and is finite at the source.

On the discrete Christoffel symbols

The piecewise flat space–time is equipped with a set of edge lengths and vertex coordinates. This defines a piecewise affine coordinate system and a piecewise affine metric in it, the discrete analogue of the unique torsion-free metric-compatible affine connection or of the Levi-Civita connection (or of the standard expression of the Christoffel symbols in terms of metric) mentioned in the literature, and, substituting this into the affine connection form of the Regge action of our previous work, we get a second-order form of the action. This can be expanded over metric variations from simplex to simplex. For a particular periodic simplicial structure and coordinates of the vertices, the leading order over metric variations is found to coincide with a certain finite difference form of the Hilbert–Einstein action.

The Fractional Form of the Tinkerbell Map Is Chaotic

This paper is concerned with a fractional Caputo-difference form of the well-known Tinkerbell chaotic map. The dynamics of the proposed map are investigated numerically through phase plots, bifurcation diagrams, and Lyapunov exponents considered from different perspectives. In addition, a stabilization controller is proposed, and the asymptotic convergence of the states is established by means of the stability theory of linear fractional discrete systems. Numerical results are employed to confirm the analytical findings.