Chaos Driven Evolutionary Algorithm: a Novel Approach for Optimization

This research deals with the initial investigations on the concept of a chaos-driven evolutionary algorithm Differential evolution. This paper is aimed at the embedding of simple two-dimensional chaotic system, which is Lozi map, in the form of chaos pseudo random number generator for Differential Evolution. The chaotic system of interest is the discrete dissipative system. Repeated simulations were performed on standard benchmark Schwefel’s test function in higher dimensions. Finally, the obtained results are compared with canonical Differential Evolution.

On the Bogolyubov endomorphisms of the renormalized square of white noise algebra

We introduce the quadratic analogue of the Bogolyubov endomorphisms of the canonical commutation relations (CCR) associated with the re-normalized square of white noise algebra (RSWN-algebra). We focus on the structure of a subclass of these endomorphisms: each of them is uniquely determined by a quadruple [Formula: see text], where [Formula: see text] are linear transformations from a test-function space [Formula: see text] into itself, while [Formula: see text] is anti-linear on [Formula: see text] and [Formula: see text] is real. Precisely, we prove that [Formula: see text] and [Formula: see text] are uniquely determined by two arbitrary complex-valued Borel functions of modulus [Formula: see text] and two maps of [Formula: see text], into itself. Under some additional analytic conditions on [Formula: see text] and [Formula: see text], we discover that we have only two equivalent classes of Bogolyubov endomorphisms, one of them corresponds to the case [Formula: see text] and the other corresponds to the case [Formula: see text]. Finally, we close the paper by building some examples in one and multi-dimensional cases.

Lump-periodic, some interaction phenomena and breather wave solutions to the (2+1)-rth dispersionless Dym equation

In this study, we successfully apply Hirota’s bilinear method (HBM) to retrieve the different wave structures of the general [Formula: see text]th dispersionless Dym equation by considering the test function approaches. The studied model is used to describe the dynamics of deep water waves. We formally retrieve some novel lump periodic, some other new interaction, and breather wave solutions. Moreover, the physical behavior of the reported results is sketched through several three-dimensional, two-dimensional and contour profiles with the assistance of suitable parameters. The acquired results are valuable in grasping the elementary scenarios of nonlinear fluid dynamics as well as the dynamics of engineering sciences in the related nonlinear higher-dimensional wave fields. The gained results are checked and found correct by putting them into the governing equation with the aid of Mathematica. Thus, our strategies through the fortress of representative calculations give a functioning and intense mathematical execution for tackling complicated nonlinear wave issues.

Nonexistence of Global Solutions to Time-Fractional Damped Wave Inequalities in Bounded Domains with a Singular Potential on the Boundary

We first consider the damped wave inequality ∂2u∂t2−∂2u∂x2+∂u∂t≥xσ|u|p,t>0,x∈(0,L), where L>0, σ∈R, and p>1, under the Dirichlet boundary conditions (u(t,0),u(t,L))=(f(t),g(t)),t>0. We establish sufficient conditions depending on σ, p, the initial conditions, and the boundary conditions, under which the considered problem admits no global solution. Two cases of boundary conditions are investigated: g≡0 and g(t)=tγ, γ>−1. Next, we extend our study to the time-fractional analogue of the above problem, namely, the time-fractional damped wave inequality ∂αu∂tα−∂2u∂x2+∂βu∂tβ≥xσ|u|p,t>0,x∈(0,L), where α∈(1,2), β∈(0,1), and ∂τ∂tτ is the time-Caputo fractional derivative of order τ, τ∈{α,β}. Our approach is based on the test function method. Namely, a judicious choice of test functions is made, taking in consideration the boundedness of the domain and the boundary conditions. Comparing with previous existing results in the literature, our results hold without assuming that the initial values are large with respect to a certain norm.

Blow-Up of Solutions to Fractional-in-Space Burgers-Type Equations

We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditions depend on the initial value and the boundary conditions. Some examples are provided to illustrate our obtained results. In the proofs of our main results, we make use of the test function method and some integral inequalities.

Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

Nonexistence of Global Solutions to Higher-Order Time-Fractional Evolution Inequalities with Subcritical Degeneracy

In this paper, we study the nonexistence of global weak solutions to higher-order time-fractional evolution inequalities with subcritical degeneracy. Using the test function method and some integral estimates, we establish sufficient conditions depending on the parameters of the problems so that global weak solutions cannot exist globally.

A Box-Girder Design Using Metaheuristic Algorithms and Mathematical Test Functions for Comparison

In engineering, metaheuristic algorithms have been used to solve complex optimization problems. This paper investigates and compares various algorithms. On one hand, the study seeks to ascertain the advantages and disadvantages of the newly presented heuristic techniques. The efficiency of the algorithms is highly dependent on the nature of the problem. The ability to change the complexity of the problem and the knowledge of global optimal locations are two advantages of using synthetic test functions for algorithm benchmarking. On the other hand, real-world design issues may frequently give more meaningful information into the effectiveness of optimization strategies. A new synthetic test function generator has been built to examine various optimization techniques. The objective function noisiness increased significantly with different transformations (Euclidean distance-based weighting, Gaussian weighting and Gabor-like weighting), while the positions of the optima remained the same. The test functions were created to assess and compare the performance of the algorithms in preparation for further development. The ideal proportions of the primary girder of an overhead crane have also been discovered. By evaluating the performance of fifteen metaheuristic algorithms, the optimum solution to thirteen mathematical optimization techniques, as well as the box-girder design, is identified. Some conclusions were drawn about the efficiency of the different optimization techniques at the test function and the transformed noisy functions. The overhead travelling crane girder design shows the real-life application.

Measuring self-reported ability to perform activities of daily living: a Rasch analysis

Background Since the number of persons diagnosed with multi-morbidity is increasing, there is a need for generic instruments to be able to assess, measure and compare ADL ability across diagnoses. Accordingly, the ADL-Interview (ADL-I) was developed to be used in rehabilitation research and clinical practice. The aim of this study was to investigate if the ADL-I can be used to provide valid and reliable ADL ability measures across gender and diagnostic groups. Methods ADL-I data were extracted from an existing research database on persons with chronic conditions including medical, rheumatological, oncological, neurological, geriatric and psychiatric diagnoses. Data were analysed based on Rasch Measurement methods to examine: the psychometric properties of the rating scale; ADL item and person fit to the Rasch model; if the difficulty of the ADL tasks differs across gender and diagnostic groups, and if the ADL-I provides precise and reliable measures of ADL ability. Results Data on n = 2098 persons were included in the final analysis. Initial evaluation of the 0–3 rating scale revealed threshold disordering between categories 1 and 2. After removal of 16 underfitting items, the variance explained by the Rasch dimension increased from 54.3 to 58.0%, thresholds were ordered, but the proportion of persons with misfitting ADL-I measures increased slightly from 8.7 to 9.1%. The person separation index improved slightly from 2.75 to 2.99 (reliability = 0.90). Differential test function analysis, however, supported that the 16 underfitting items did not represent a threat to the measurement system. Similarly, ADL items displaying differential item functioning across gender and diagnoses did not represent a threat to the measurement system. The ADL items and participants were well distributed along the scale, with item and person measures well targeted to each other, indicating a small ceiling effect and no floor effect. Conclusions The study results overall suggest that the ADL-I is producing valid and reliable measures across gender and diagnostic groups among persons within a broad range of ADL ability, providing evidence to support generic use of the ADL-I. Trial registration N/A.

RESEARCH AND DIAGNOSTICS FOR THE LABORATORY OF PRESSURE RESISTANT SENSORS

The use of the sensors shortens the service life, wears out and reduces their accuracy due to operation. For sensors with a susceptibility to inaccuracy, it is possible to create a sensor-device-software diagnostic set. Such a scheme of configuration should be able to provide autonomic diagnostic, calibration, evaluation and also recalibration of the sensor. The diagnostic equipment could also have a shock test function in order to intentionally and faster reduce the service life and thus test the correctly set parameters of the diagnostic algorithm in laboratory conditions. The diagnostic device is a specialized technical system that provides conditions for the future potential of the testing development, knowledge and experience. According to the design, it can be modularly enriched with new parts, fixtures and systems to provide a more diverse range of options. There would be space for exploring the possibilities of new types of sensors, their comparison, as well as full-fledged automation of the complex diagnostic process.