A fixed point theorem for contractions in modular metric spaces

The notion of a (metric) modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by the author [V. V. Chistyakov, Metric modulars and their application, Dokl. Math. 73(1) (2006) 32-35, and Modular metric spaces, I: Basic concepts, Nonlinear Anal. 72(1) (2010) 1-14]. In this paper we establish a fixed point theorem for contractive maps in modular spaces. It is related to contracting rather ``generalized average velocities'' than metric distances, and the successive approximations of fixed points converge to the fixed points in a weaker sense as compared to the metric convergence.Comment: 31 pages, LaTeX, uses elsarticle.st

The Glacier Complexes of the Mountain Massifs of the North-West of Inner Asia and their Dynamics

The subject of this paper is the glaciation of the mountain massifs Mongun-Taiga, Tavan-Boghd-Ola, Turgeni- Nuru, and Harhira-Nuru. The glaciation is represented mostly by small forms that sometimes form a single complex of domeshaped peaks. According to the authors, the modern glaciated area of the mountain massifs is 21.2 km2 (Tavan-Boghd-Ola), 20.3 km2 (Mongun-Taiga), 42 km2 (Turgeni- Nuru), and 33.1 km2 (Harhira-Nuru). The area of the glaciers has been shrinking since the mid 1960’s. In 1995–2008, the rate of reduction of the glaciers’ area has grown considerably: valley glaciers were rapidly degrading and splitting; accumulation of morainic material in the lower parts of the glaciers accelerated. Small glaciers transformed into snowfields and rock glaciers. There has been also a degradation of the highest parts of the glaciers and the collapse of the glacial complexes with a single zone of accumulation into isolated from each other glaciers. Reduced snow cover area has led to a rise in the firn line and the disintegration of a common accumulation area of the glacial complex. In the of the Mongun-Taiga massif, in 1995– 2008, the firn line rose by 200–300 m. The reduction of the glaciers significantly lagged behind the change in the position of the accumulation area boundary. In the past two years, there has been a significant recovery of the glaciers that could eventually lead to their slower degradation or stabilization of the glaciers in the study area

Thermal Emission Control via Twist Tuning of Embedded Eigenstates

The field of thermal emission engineering shows great potential for various applications, such as lighting, energy harvesting, and imaging, using natural or artificial structures. However, existing structures face challenges in fabrication or do not provide the necessary degree of control over key parameters such as emission intensity, spectral composition, and angular distribution. To address these limitations, we propose a novel approach that leverages in-plane hyperbolic response, embedded eigenstates enabled by epsilon-near-zero, and exceptional tunability through twisting in {\alpha}-MoO3 heterostructures. By adjusting the twist angle, we can manipulate the system's properties, transforming it from a near-perfect reflector to a perfect absorber. This enables us to exert control over thermal emission power, spanning an order of magnitude. Furthermore, our research has uncovered a significant angular dependence of thermal emission, which varies with relative rotation