A Result on Convergence of Sequences of Iterations with Applications to Best-Response Dynamics

The result that says the sequence of iterations [Formula: see text] converges if [Formula: see text] is an increasing function has numerous applications in elementary economic analysis. I generalize this simple result to some mappings [Formula: see text]. The applications of the new result include the convergence of the best-response dynamics in the general version of the Crawford and Sobel model and in some versions of the Hotelling and Tiebout models.

Prejudice and discrimination relating to covid-19 in Bangladesh’s perspective

Covid-19 raised indeed prejudice among people than ever before what should never be taken for granted; the author intended to identify the circumstance of prejudice touching Covid-19 in Bangladesh. In this study, the author used the qualitative method of research to analyze and discuss data narratively. This study found out a simple result which is people relating to Covid-19, from the very beginning, were subjected to brutal and humiliating treatment. Other specific findings are- with a few exceptions, people were associated with prejudice about Covid-19; people did whatever they want without thinking the perilous situation of Covid-19 infected patients and dead body; as doctors and nurses treated infected patients, the neglect they had similarly suffered; the family of Covid-19 infected people also faced negligent practices of neighbors after the other. In this case, the sufferers couldn’t wait indefinitely and the policymakers of Bangladesh had a lot more to do while there is still time. Therefore, they took more effective and urgent actions which can be a wake-up call on how people should behave to make a greener future. This study will help researchers, academicians, and policymakers with providing valuable information about the situation of prejudice about Covid-19 in Bangladesh.

Prejudice and Discrimination Relating to Covid-19 in Bangladesh’s Perspective

Covid-19 raised indeed prejudice among people than ever before what should never be taken for granted; the author intended to identify the circumstance of prejudice touching Covid-19 in Bangladesh. In this study, the author used the qualitative method of research to analyze and discuss data narratively. This study found out a simple result which is people relating to Covid-19, from the very beginning, were subjected to brutal and humiliating treatment. Other specific findings are- with a few exceptions, people were associated with prejudice about Covid-19; people did whatever they want without thinking the perilous situation of Covid-19 infected patients and dead body; as doctors and nurses treated infected patients, the neglect they had similarly suffered; the family of Covid-19 infected people also faced negligent practices of neighbors after the other. In this case, the sufferers couldn’t wait indefinitely and the policymakers of Bangladesh had a lot more to do while there is still time. Therefore, they took more effective and urgent actions which can be a wake-up call on how people should behave to make a greener future. This study will help researchers, academicians, and policymakers with providing valuable information about the situation of prejudice about Covid-19 in Bangladesh.

Prejudice and Discrimination Relating to Covid-19 in Bangladesh’s Perspective

Covid-19 raised indeed prejudice among people than ever before what should never be taken for granted; the author intended to identify the circumstance of prejudice touching Covid-19 in Bangladesh. In this study, the author used the qualitative method of research to analyze and discuss data narratively. This study found out a simple result which is people relating to Covid-19, from the very beginning, were subjected to brutal and humiliating treatment. Other specific findings are- with a few exceptions, people were associated with prejudice about Covid-19; people did whatever they want without thinking the perilous situation of Covid-19 infected patients and dead body; as doctors and nurses treated infected patients, the neglect they had similarly suffered; the family of Covid-19 infected people also faced negligent practices of neighbors after the other. In this case, the sufferers couldn’t wait indefinitely and the policymakers of Bangladesh had a lot more to do while there is still time. Therefore, they took more effective and urgent actions which can be a wake-up call on how people should behave to make a greener future. This study will help researchers, academicians, and policymakers with providing valuable information about the situation of prejudice about Covid-19 in Bangladesh.

A Topological Coincidence Theory for Multifunctions via Homotopy

A new simple result is presented which immediately yields the topological transversality theorem for coincidences.

Invariant measures for interval translations and some other piecewise continuous maps

We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation maps) a Borel probability non-atomic invariant measure exists for any map. We use this result to demonstrate that any interval translation map endowed with such a measure is metrically equivalent to an interval exchange map. Finally, we study the general case of piecewise continuous maps and prove a simple result on existence of an invariant measure provided all discontinuity points are wandering.

Hardware Trojans detection in chaos-based cryptography

The paper deals with the security problems in chaotic-based cryptography. In particular, the 0–1 test for chaos is used to detect hardware Trojans in electronic circuits – generators of chaotic bit sequences. The proposed method of detecting hardware Trojans is based on analyzing the original bit sequences through the 0–1 test yielding a simple result, either a number close to 1, when the examined bit sequence is chaotic, or a number close to 0, when the sequence is non-chaotic. A complementary result is a graph of translation variables qc and pc which form a basis of the 0–1 test. The method does not require any extra corrections and can be applied to relatively short sequences of bits. This makes the method quite attractive as the security problems are dealt with at the chaotic generator level, with no need to apply any extractors of randomness. The method is illustrated by numerical examples of simulated Trojans in chaotic bit generators based on the analog Lindberg circuit as well as a discrete system based on the logistic map.

BQ-Semigroups of Generalised Linear Transformations

If V and W are vector spaces over the same field, we let T(V,W) denote the set of all linear transformations from V into W. In addition, if θ ∈ T(W,V), we define a “sandwich operation” ∗ on T(V,W) by α ∗ β=α θ β for all α, β ∈ T(V,W). Then (T(V,W),∗) is a semigroup of so-called generalised linear transformations, which we denote by T(V,W,θ). A simple result for abstract semigroups shows that T(V,W,θ) belongs to the class BQ of all semigroups whose sets of bi-ideals and quasi-ideals coincide. In recent work, Mendes-Gonçalves and Sullivan examined the same problem for subsemigroups S of T(V,V, id V) for which the dimension (or codimension) of the kernel (or the range) of each α ∈ S is bounded by a fixed cardinal. Here we extend that work to certain subsemigroups of T(V,W,θ) where V ≠ W.