On A Logarithmic Mittag-Leffler Function, its Properties and Applications

In this paper, we introduce a logarithmic Mittag-Leffler function and discuss some of its properties. The application of these properties become helpful in extension of Pochhammer’s type contour integral representations and Rodrigues formulae of some known hypergeometric functions. On application point of view, some relations are discussed which are useful in interpreting the phenomenon of spread of infectious diseases in terms of Lauricella’s multiple hypergeometric functions.

Assessment of OpenMP Master–Slave Implementations for Selected Irregular Parallel Applications

The paper investigates various implementations of a master–slave paradigm using the popular OpenMP API and relative performance of the former using modern multi-core workstation CPUs. It is assumed that a master partitions available input into a batch of predefined number of data chunks which are then processed in parallel by a set of slaves and the procedure is repeated until all input data has been processed. The paper experimentally assesses performance of six implementations using OpenMP locks, the tasking construct, dynamically partitioned for loop, without and with overlapping merging results and data generation, using the gcc compiler. Two distinct parallel applications are tested, each using the six aforementioned implementations, on two systems representing desktop and worstation environments: one with Intel i7-7700 3.60GHz Kaby Lake CPU and eight logical processors and the other with two Intel Xeon E5-2620 v4 2.10GHz Broadwell CPUs and 32 logical processors. From the application point of view, irregular adaptive quadrature numerical integration, as well as finding a region of interest within an irregular image is tested. Various compute intensities are investigated through setting various computing accuracy per subrange and number of image passes, respectively. Results allow programmers to assess which solution and configuration settings such as the numbers of threads and thread affinities shall be preferred.

Ultrastiff graphene

Graphene has exceptionally high in-plane strength, which makes it ideal for various nanomechanical applications. At the same time, its exceptionally low out-of-plane stiffness makes it also flimsy and hard to handle, rendering out-of-plane structures unstable and difficult to fabricate. Therefore, from an application point of view, a method to stiffen graphene would be highly beneficial. Here we demonstrate that graphene can be significantly stiffened by using a laser writing technique called optical forging. We fabricate suspended graphene membranes and use optical forging to create stable corrugations. Nanoindentation experiments show that the corrugations increase graphene bending stiffness up to 0.8 MeV, five orders of magnitude larger than pristine graphene and corresponding to some 35 layers of bulk graphite. Simulations demonstrate that, in addition to stiffening by micron-scale corrugations, optical forging stiffens graphene also at the nanoscale. This magnitude of stiffening of an atomically thin membrane will open avenues for a plethora of new applications, such as GHz resonators and 3D scaffolds.

The Complex Order Fractional Derivatives and Systems Are Non Hermitian

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Strength of structural ice protection for steering and propulsion units

Steering and propulsion are one of the most vulnerable elements of ice-going ships. This paper discusses structural ice protection for steering and propulsion units suggested and patented by the authors. This system protects rudder blade from the stern over its whole height. The paper gives the results of strength study for this structure depending on relative size of its elements, their stiffness ratios, as well as on application point and direction of ice load.

Implicit max-stable extremal integrals

Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function f ≥ 0. From an application point of view, one is rather interested in extreme loss events that occur relative to f than in the corresponding extreme values itself. In this context, so-called f -implicit α-Fréchet max-stable distributions arise and have been used to construct independently scattered sup-measures that possess such margins. In this paper we solve an open problem in Goldbach (2016) by developing a stochastic integral of a deterministic function g ≥ 0 with respect to implicit max-stable sup-measures. The resulting theory covers the construction of max-stable extremal integrals (see Stoev and Taqqu Extremes 8, 237–266 (2005)) and, at the same time, reveals striking parallels.

Recent Progress in the Detection of Bacteria Using Bacteriophages: A Review

Bacteria will likely become our most significant enemies of the 21st century, as we are approaching a post-antibiotic era. Bacteriophages, viruses that infect bacteria, allow us to fight infections caused by drug-resistant bacteria and create specific, cheap, and stable sensors for bacteria detection. Here, we summarize the recent developments in the field of phage-based methods for bacteria detection. We focus on works published after mid-2017. We underline the need for further advancements, especially related to lowering the detection (below 1 CFU/mL; CFU stands for colony forming units) and shortening the time of analysis (below one hour). From the application point of view, portable, cheap, and fast devices are needed, even at the expense of sensitivity.

Visualization of the Chaos Game for non-hyperbolic iterated function system

The chaos game is a random algorithm generally applied to contracting (hyperbolic) iterated function system (IFS) which makes it possible to obtain the unique attractor of the dynamic system. However, when applied to non-contractive IFS extremely interesting results can be obtained that are not only important from a theoretical and application point of view, but can also be part of a mathematical didactics that seeks to modernize teaching. In this sense, this research present some results related to the application of the chaos game to non-contracting IFS are presented.

Promiscuous esterases counterintuitively are less flexible than specific ones

Understanding mechanisms of promiscuity is increasingly important from a fundamental and application point of view. As to enzyme structural dynamics, more promiscuous enzymes generally have been recognized to also be more flexible. However, examples for the opposite received much less attention. Here, we exploit comprehensive experimental information on the substrate promiscuity of 147 esterases tested against 96 esters together with computationally efficient rigidity analyses to understand the molecular origin of the observed promiscuity range. Unexpectedly, our data reveal that promiscuous esterases are significantly less flexible than specific ones, are significantly more thermostable, and have a significantly increased specific activity. These results may be reconciled with a model according to which structural flexibility in the case of specific esterases serves for conformational proofreading. Our results signify that esterase sequence space can be screened by rigidity analyses for promiscuous esterases as starting points for further exploration in biotechnology and synthetic chemistry.