This paper presents a method of component testing based on algebraic specifications. An algorithm for generating checkable test cases is proposed. A prototype tool called CASCAT Java Enterprise Beans developed. It has the advantages high degree automation, which include case generation, harness construction and result checking. achieves scalability by allowing incremental integration. also allows to focus subset used functions key properties, thus suitable testing. The reports an...

The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems nonlocal dispersal in time space periodic habitats. notion speed intervals such a system first introduced via natural features speeds. lower bounds are then established. When dependence habitat only on variable, single proved. It also shows that, under certain conditions, interval any direction singleton, and, moreover, holds.

Algebraic testing is an automated software method based on algebraic formal specifications. It has the advantages of highly process and independence software's implementation details. This paper applies to components. An tool called CASCAT for Java components presented. A case study shows high fault detecting ability.

The current paper is concerned with positive stationary solutions and spatial spreading speeds of KPP type evolution equations local (i.e. the standard Laplacian) or nonlocal discrete dispersal in locally spatially inhomogeneous media.It shown that such an equation has a unique globally stable solution speed every direction.Moreover, it localized inhomogeneity medium neither slows down nor up all directions.

<abstract><p>In this article, we constructed a derivative-free family of iterative techniques for extracting simultaneously all the distinct roots non-linear polynomial equation. Convergence analysis is discussed to show that proposed method has fifth order convergence. Nonlinear test models including fractional conversion, predator-prey, chemical reactor and beam designing are included. Also many other interesting results concerning symmetric problems with application group...

<abstract><p>This study shows the link between computer science and applied mathematics. It conducts a dynamics investigation of new root solvers using tools develops family single-step simple root-finding methods. The convergence order proposed iterative methods is two, according to analysis carried out symbolic computation in algebra system CAS-Maple 18. Without further evaluations given nonlinear function its derivatives, very rapid rate achieved, demonstrating remarkable...

AbstractThe COVID-19 pandemic, like past historical events such as the Vietnam War or 9/11, will shape a generation. Mathematics educators can seize this unprecedented opportunity to teach principles of mathematical modeling in epidemiology. Compartmental epidemiological models, SIR (susceptible-infected-recovered), are widely used by researchers and study infectious disease dynamics, particularly for COVID-19. The model is considered fundamental spread epidemic employs Ordinary Differential...

Accurate forecasting of the coronavirus disease 2019 (COVID-19) spread is indispensable for effective public health planning and allocation healthcare resources at all levels governance, both nationally globally. Conventional prediction models COVID-19 pandemic often fall short in precision, due to their reliance on homogeneous time-dependent transmission rates oversight geographical features when isolating study regions. To address these limitations advance predictive capabilities models,...

This paper presents a high-directionality optical grating antenna for chip-level LiDAR applications. The antenna, designed on silicon-nitride-nitride platform, consists of two vertically stacked layers with nitride waveguide layer in between. By optimizing the periods, duty cycles, and relative offset between using particle swarm optimization algorithm, directionality 87.8% (0.56 dB) at 1550 nm wavelength minimum coupling loss 1.7 dB were achieved. performance was demonstrated chip-to-chip...

The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems nonlocal dispersal in time space periodic habitats. notion speed intervals such a system first introduced via natural features speeds. lower bounds are then established. When dependence habitat only on variable, single proved. It also shows that, under certain conditions, interval any direction singleton, and, moreover, holds.

The current paper is concerned with positive stationary solutions and spatial spreading speeds of KPP type evolution equations random or nonlocal discrete dispersal in locally spatially inhomogeneous media. It shown that such an equation has a unique globally stable solution speed every direction. Moreover, it the localized inhomogeneity medium neither slows down nor up all directions.

The current paper investigate the persistence of positive solutions KPP type evolution equations with random/nonlocal dispersal in locally spatially inhomogeneous habitat. By constructions super/sub and comparison principle, we prove that such an equation has a unique globally stable stationary solution.

The paper introduces a new method of option pricing which is insurance accurate calculation. It to deal with the problems under unbalance, arbitrage existing and incomplete circumstance. Meanwhile this transforms into problem equivalent fair premium. This approach valid even when exists market unbalanced. proved that subject matters saltant price like agricultural product can be priced well by model jump-diffusion process, in paper, "abnormal" fluctuate described renewal process more general...

This paper is concerned with the asymptotic dynamics of two species competition systems form $ \begin{equation*} \begin{cases} u_t(t,x) = \mathcal{A} u+u(a_1(t,x)-b_1(t,x)u-c_1(t,x)v),\quad x\in {\mathbb{R}} \cr v_t(t,x) v+ v(a_2(t,x)-b_2(t,x)u-c_2(t,x) v),\quad \end{cases} \end{equation*} where (\mathcal{A}u)(t,x) u_{xx}(t,x) $, or \int_{ }\kappa(y-x)u(t,y)dy-u(t,x) ($ \kappa(\cdot) a smooth non-negative convolution kernel supported on an interval centered at origin), a_i(t+T,x) a_i(t,x)...

In this paper, we consider a monostable model with hybrid dispersal. This characterizes the time evolution of population which disperses both locally and nonlocally in spatially inhomogeneous media. It is shown that such equation has spreading speed every direction.