On logarithmic Hölder continuity of mappings on the boundary

We study mappings satisfying the so-called inverse Poletsky inequality. Under integrability of the corresponding majorant, it is proved that these mappings are logarithmic Hölder continuous in the neighborhood of the boundary points. In particular, the indicated properties hold for homeomorphisms whose inverse satisfy the weighted Poletsky inequality.

Characteristic form of dynamics equations of Cosserat medium

In this paper, we construct the characteristic form of the equations of dynamics of the Cosserat medium and the Cosserat pseudocontinuum for bounded bodies. The method of matrix transformations proposed by the author is used for construction and allows obtaining the necessary relations using identical transformations. The obtained equations are compared with those for a symmetrically elastic isotropic homogeneous body. A method is proposed for selecting the necessary equations for computational schemes at the internal and boundary points of the body. A sequence of operations is proposed for iterative calculations of stresses, particle velocities, moment stresses, and angular velocities of particles in a coupled model of the Cosserat medium.

PROCESSING OF HARDENED CYLINDRICAL GEAR WHEELS OF THE CUTTING GEARBOX OF THE COMBINE UKD 200-500

The article discusses the latest developments of unique technological methods of gear milling of cylindrical gears for preliminary blade gear processing of hardened cylindrical gears of the cutting reducer of the UKD200-500 coal mining harvester for the final gear grinding of gear teeth with modulus m = 16 mm, with hardness HRC 56 ... 62. The peculiarity of the design of special hob cutters is that a circle passing through the lower boundary points of the involute is used as the palloid of the machine gearing of the tool and part. Pre-cutting the teeth of hardened wheels with carbide milling cutters allows you to remove the main allowance for the final gear grinding.

ON THE BOUNDARY BEHAVIOUR OF FRIDMAN INVARIANTS

We prove that the Fridman invariant defined using the Carathéodory pseudodistance does not always go to 1 near strongly Levi pseudoconvex boundary points and it always goes to 0 near nonpseudoconvex boundary points. We also discuss whether Fridman invariants can be extended continuously to some boundary points of domains constructed by deleting compact subsets from other domains.

Semiregular and strongly irregular boundary points for p-harmonic functions on unbounded sets in metric spaces

The trichotomy between regular, semiregular, and strongly irregular boundary points for $$p$$ p -harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $$p$$ p -Poincaré inequality, $$1<p<\infty $$ 1 < p < ∞ . We show that these are local properties. We also deduce several characterizations of semiregular points and strongly irregular points. In particular, semiregular points are characterized by means of capacity, $$p$$ p -harmonic measures, removability, and semibarriers.

Weather Prediction and Smart Notification System

In the recent period, many real-world applications and institutions generates a huge amount of data which is unstructured i.e., in the form of images containing data, receipts, invoices, forms, statements, contracts etc. This rich and detailed information presented in the text is of great significance in computer vision-based applications (driverless cars, assisting blind and visually impaired people, detecting labels and packages, automatic number plate recognition etc.). Recently, there has been a hike in the efforts, researches and progresses being done in this domain for its significance in data analysis and computer vision. Here has been a diversity of challenges in unstructured data like image sensor noise, different viewing angles, blur, lighting conditions, resolution, and non-planar object. Our objective for taking up this topic for research are i) to detect and recognize the text from the data ii) to handle diversity and variability of text in natural scene iii) to explore various datasets iv) to deal with various issues occurring in scene text detection. To tackle this problem, we propose a robust scene text detection and recognition method with adaptive text region representation using deep learning model open CV with EAST algorithm as detection pipeline and tesseract. The recurrent neural network-based adaptive text region representation is proposed for text region refinement, where a pair of boundary points are predicted each time step until no new points are found. In this way, text regions in an image are detected and represented with the adaptive number of boundary points.

Homogeneous Plurisubharmonic Polynomials in Higher Dimensions

We prove several results on homogeneous plurisubharmonic polynomials on $${\mathbb {C}}^n$$ C n , $$n\in {\mathbb {Z}}_{\ge 2}$$ n ∈ Z ≥ 2 . Said results are relevant to the problem of constructing local bumpings at boundary points of pseudoconvex domains of finite D’Angelo 1-type in $${\mathbb {C}}^{n+1}$$ C n + 1 .