NEW SOLUTION TO THE PROBLEM OF A CRACK IN AN ORTHOTROPIC PLATE UNDER TENSION

Abstract— A classical plane problem of the theory of elasticity about a crack in a stretched orthotropic elastic unbounded plane is considered, which leads to a singular solution for stresses in the vicinity of the crack edge. The relations of the generalized theory of elasticity, including a small scale parameter, are given. The equations of the generalized theory are of a higher order than the equations of the classical theory and allow eliminating the singularity of the classical solution. The scale parameter is determined experimentally. The results obtained determine the effect of the crack length on the bearing capacity of the plate and are compared with the experimental results for plates made of fiberglass and carbon fiber reinforced plastic.

Classification of Stable Solutions to a Non-Local Gelfand–Liouville Equation

We study finite Morse index solutions to the non-local Gelfand–Liouville problem $$\begin{align*}& (-\Delta)^su=e^u\quad\textrm{in}\quad{{\mathbb{R}}^n}, \end{align*}$$for every $s\in (0,1)$ and $n>2s$. Precisely, we prove non-existence of finite Morse index solutions whenever the singular solution $$\begin{align*} &u_{n,s}(x)=-2s\log|x|+\log \left(2^{2s}\frac{\Gamma(\frac{n}{2})\Gamma(1+s)}{\Gamma(\frac{n-2s}{2})}\right)\end{align*}$$is unstable.

Design of an Offline Handwriting Recognition System Tested on the Bangla and Korean Scripts

This dissertation presents a flexible and robust offline handwriting recognition system which is tested on the Bangla and Korean scripts. Offline handwriting recognition is one of the most challenging and yet to be solved problems in machine learning. While a few popular scripts (like Latin) have received a lot of attention, many other widely used scripts (like Bangla) have seen very little progress. Features such as connectedness and vowels structured as diacritics make it a challenging script to recognize. A simple and robust design for offline recognition is presented which not only works reliably, but also can be used for almost any alphabetic writing system. The framework has been rigorously tested for Bangla and demonstrated how it can be transformed to apply to other scripts through experiments on the Korean script whose two-dimensional arrangement of characters makes it a challenge to recognize. The base of this design is a character spotting network which detects the location of different script elements (such as characters, diacritics) from an unsegmented word image. A transcript is formed from the detected classes based on their corresponding location information. This is the first reported lexicon-free offline recognition system for Bangla and achieves a Character Recognition Accuracy (CRA) of 94.8%. This is also one of the most flexible architectures ever presented. Recognition of Korean was achieved with a 91.2% CRA. Also, a powerful technique of autonomous tagging was developed which can drastically reduce the effort of preparing a dataset for any script. The combination of the character spotting method and the autonomous tagging brings the entire offline recognition problem very close to a singular solution. Additionally, a database named the Boise State Bangla Handwriting Dataset was developed. This is one of the richest offline datasets currently available for Bangla and this has been made publicly accessible to accelerate the research progress. Many other tools were developed and experiments were conducted to more rigorously validate this framework by evaluating the method against external datasets (CMATERdb 1.1.1, Indic Word Dataset and REID2019: Early Indian Printed Documents). Offline handwriting recognition is an extremely promising technology and the outcome of this research moves the field significantly ahead.

The Need for Increasing Black Entrepreneurship as a Result of the COVID-19 Pandemic

COVID-19 and recent high-profile police killings are putting focus on the inequities and societal hurdles facing blacks in the U.S. There is no quick fix or singular solution; however, increasing black entrepreneurship may be a key piece of the solution. The reasons for, and potential benefits of, new public policies and private investment to spur black entrepreneurship are discussed.

Two Flavors of Hydrogen Atoms: A Possible Explanation of Dark Matter

In one of our previous papers, it was shown that for the ground state of hydrogenic atoms/ions, it is possible to match the interior (inside the nucleus) solution of the Dirac equation with the singular exterior solution of the Dirac equation, so that the singular solution should not be rejected for the ground state of hydrogenic atoms/ions. In that paper, there was presented also the first experimental proof of the existence of this Alternative Kind of Hydrogen Atoms (AKHA)—by showing that the presence of the AKHA solves a long-standing mystery of the huge discrepancy between the experimental and previous theoretical results concerning the high-energy tail of the linear momentum distribution in the ground state of hydrogen atoms. In another paper, we showed that for hydrogen atoms, the singular solution of the Dirac equation outside the proton is legitimate not just for the ground state 12S1/2, but also for the states 22S1/2, 32S1/2 and so on: it is legitimate for all the discrete states n2S1/2. Moreover, the singular exterior solution is legitimate also for the l = 0 states of the continuous spectrum. In that paper, we demonstrated that the AKHA can be the basis for explaining the recent puzzling astrophysical observational results concerning the redshifted radio line 21 cm from the early Universe. Thus, there seems to be the astrophysical evidence of the existence of the AKHA—in addition to the already available observational proof of their existence from atomic experiments. In the present paper, we point out that the AKHA provide an alternative view on dark matter—without resorting to new subatomic particles or dramatically changing the existing physical laws. This is because due to the selection rules, the AKHA do not have state that can be coupled by the electric dipole radiation. We also reformulate the above theoretical results in terms that hydrogen atoms can have two flavors: one flavor corresponding to the regular solution outside the proton, another—to the singular solution outside the proton, both solutions corresponding to the same energy. Since this means the additional degeneracy, then according to the fundamental theorem of quantum mechanics, there should be an additional conserved quantity, which we call isohydrogen spin (isohyspin). Further atomic experiments for accurately measuring the high-energy tail of the linear momentum distribution in the ground state of hydrogen atoms, as well as further observational studies of the redshifted 21 cm radio line from the early Universe, could provide a further proof that dark matter or a part of it is the AKHA.