This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order $\mathcal{O} (\sqrt{\varepsilon})$, where $\varepsilon$ is the perturbation parameter.

Organizations can improve efficiency of process execution through a correct resource allocation, as well as increase income, improve client satisfaction, and so on. This work presents a novel approach for solving problems of resource allocation in business processes which combines process mining, statistical techniques, and metaheuristic algorithms for optimization. In order to get more reliable results of the simulation, in this paper, we use process mining analysis and statistical techniques for building a simulation model. For finding optimal human resource allocation in business processes, we use the improved differential evolution algorithm with population adaptation. Because of the use of a stochastic simulation model, noise appears in the output of the model. The differential evolution algorithm is modified in order to include uncertainty in the fitness function. In the end, validation of the model was done on three different data sets in order to demonstrate the generality of the approach, and the comparison with the standard approach from the literature was done. The results have shown that this novel approach gives solutions which are better than the existing model from literature.

The aim of this research was to find the relationship between metals content and age of the sediment and to estimate the contamination level. For the research of sediment, samples were taken from the glacial Lake Prokosko. Concentrations of eight elements (Ca, Mg, Fe, Cd, Pb, Zn, Cu and Mn) were determined. The age was determined with usage of C14. For statistical evaluation of the results, we used basic statistical tools, correlation, and PCA. The results showed that all of investigated metals have natural origin. Sediment core from this research was around 18,000 years old and the results revealed characteristics of metals deposition in the process of sedimentation. Concentrations of metals were compared with age (depth) of sediment. Maximal concentrations for iron, calcium, magnesium and manganese are found in the period of Allerӧd oscilation. Differences in Mn/Fe ratio and organic matter content are showing changes through history. These results show metal deposition characteristics in different climate periods, and these characteristics could be used as another proof of climate change.

Grasping objects under uncertainty remains an open problem in robotics research. This uncertainty is often due to noisy or partial observations of the object pose or shape. To enable a robot to react appropriately to unforeseen effects, it is crucial that it continuously takes sensor feedback into account. While visual feedback is important for inferring a grasp pose and reaching for an object, contact feedback offers valuable information during manipulation and grasp acquisition. In this paper, we use model-free deep reinforcement learning to synthesize control policies that exploit contact sensing to generate robust grasping under uncertainty. We demonstrate our approach on a multi-fingered hand that exhibits more complex finger coordination than the commonly used two-fingered grippers. We conduct extensive experiments in order to assess the performance of the learned policies, with and without contact sensing. While it is possible to learn grasping policies without contact sensing, our results suggest that contact feedback allows for a significant improvement of grasping robustness under object pose uncertainty and for objects with a complex shape.

We report on a numerical study of the vortex structure modifications and drag reduction in a flow over a rotationally oscillating circular cylinder at a high subcritical Reynolds number, $Re=1.4\times 10^{5}$ . Considered are eight forcing frequencies $f=f_{e}/f_{0}=0.5$ , $1$ , $1.5$ , $2$ , $2.5$ , $3$ , $4$ , $5$ and three forcing amplitudes $\unicode[STIX]{x1D6FA}=\unicode[STIX]{x1D6FA}_{e}D/2U_{\infty }=1$ , $2$ , $3$ , non-dimensionalized with $f_{0}$ , which is the natural vortex-shedding frequency without forcing, $U_{\infty }$ the free-stream velocity, $D$ the diameter of the cylinder. In order to perform a parametric study of a large number of cases ( $24$ in total) with affordable computational resources, the three-dimensional unsteady computations were performed using a wall-integrated (WIN) second-moment (Reynolds-stress) Reynolds-averaged Navier–Stokes (RANS) turbulence closure, verified and validated by a dynamic large-eddy simulations (LES) for selected cases ( $f=2.5$ , $\unicode[STIX]{x1D6FA}=2$ and $f=4$ , $\unicode[STIX]{x1D6FA}=2$ ), as well as by the earlier LES and experiments of the flow over a stagnant cylinder at the same $Re$ number described in Palkin et al. (Flow Turbul. Combust., vol. 97 (4), 2016, pp. 1017–1046). The drag reduction was detected at frequencies equal to and larger than $f=2.5$ , while no reduction was observed for the cylinder subjected to oscillations with the natural frequency, even with very different values of the rotation amplitude. The maximum reduction of the drag coefficient is 88 % for the highest tested frequency $f=5$ and amplitude $\unicode[STIX]{x1D6FA}=2$ . However, a significant reduction of 78 % appears with the increase of $f$ already for $f=2.5$ and $\unicode[STIX]{x1D6FA}=2$ . Such a dramatic reduction in the drag coefficient is the consequence of restructuring of the vortex-shedding topology and a markedly different pressure field featured by a shrinking of the low pressure region behind the cylinder, all dictated by the rotary oscillation. Despite the need to expend energy to force cylinder oscillations, the considered drag reduction mechanism seems a feasible practical option for drag control in some applications for $Re>10^{4}$ , since the calculated power expenditure for cylinder oscillation under realistic scenarios is several times smaller than the power saved by the drag reduction.

In this paper, we investigate the bandwidth and power allocation problem in remote radio head cluster (RRHC)-based millimeter wave (mm-wave) massive MIMO heterogeneous cloud radio access networks with limited fronthaul capacity. The coordinated multipoint transmission is applied in each RRHC for cancelling the intra-cluster interference. To avoid the inter-tier interference, distinct bandwidths are allocated to macro base station and RRHs. Following this, we formulate a bandwidth and power allocation optimization problem to maximize the downlink weighted sum rate of the system subject to per-RRHC power and fronthaul capacity constraints, which is a non-convex optimization problem and is difficult to directly solve. Next, we fix the bandwidth allocation and the original problem can be divided into two independent optimization problems, i.e., the weighted sum rate maximization problems of MUs and RRH users, respectively. For the former, the convex optimization technique can be used to solve it. As for the latter, a two-loop iterative algorithm is proposed to deal with it. Specifically, we propose the price-based outer iteration to control the fronthaul capacity and the weighted minimum mean square error-based inner iteration to obtain the power allocation. To this end, a 1-D search method is adopted to find the optimal bandwidth allocation. Finally, numerical results are conducted to verify the effectiveness of the proposed algorithms under different parameters.

Biodizel je naziv za gorivo dobiveno iz obnovljivih izvora koje se može upotrebljavati u nemodificiranim dizelskim motorima umjesto uobičajenog fosilnog dizelskog goriva. Biodizel je ustvari komercijalni naziv za smjesu metilnog estera, koja se danas može naći na tržištu tekućih goriva, prije svega u EU-u, gdje se i prodaje krajnjim korisnicima. Globalna proizvodnja biodizela u 2014. godini premašila je 30 milijardi litara od čega oko 39 % otpada na EU.1 Kao osnovna sirovina za dobivanje biodizela mogu poslužiti svi izvori biomase bogati triacilglicerolima. U prvom redu tu spadaju jestiva biljna ulja, zatim nejestiva, otpadna i upotrijebljena ulja, kao i životinjske masti. Metanoliza biljnih ulja može biti podijeljena na osnovu prisutnosti i vrste katalizatora ili topljivosti katalizatora u reakcijskoj smjesi. Ovisno o tome odvija li se reakcija metanolize s ili bez prisutnosti katalizatora, metanoliza može biti katalizirana i nekatalizirana. Kemijski katalizatori metanolize razlikuju se kako po svojoj prirodi tako i na osnovi njihove topljivosti u reakcijskoj smjesi. Ovisno o tome je li katalizator u reakcijskoj smjesi topljiv ili nije, kemijski katalizirana metanoliza može biti podijeljena na homogeno, heterogeno i homogeno-heterogeno kataliziranu metanolizu. Osnovna karakteristika homogeno katalizirane metanolize je otopljen katalizator u reakcijskoj smjesi. Homogeni katalizatori metanolize mogu biti lužine i kiseline. Najčešće istraživan i u komercijalnim procesima najčešće primjenjivan način dobivanja biodizela je metanoliza katalizirana lužinama. Proces transesterifikacije s lužnatim katalizatorom uobičajen je način proizvodnje biodizela iz rafiniranih biljnih ulja. Kao lužnati katalizatori najčešće se upotrebljavaju kalijev hidroksid (KOH), natrijev hidroksid (NaOH) i natrijev metoksid (NaOCH3). Unatoč brojnim prednostima homogeno katalizirane metanolize, glavni nedostatak joj je nemogućnost ponovne uporabe katalizatora. Pored toga, katalizator zaostaje u esterskoj frakciji, odakle ga je potrebno ukloniti, što se najčešće provodi višestrukim ispiranjem s vodom, a otpadna voda čini značajan problem za okoliš.2,3 Uporabom katalizatora koji se ne otapaju u reakcijskoj smjesi, pojednostavljuje se način izdvajanja i rafiniranja proizvoda, smanjuju okolišni problemi i omogućava ponovna uporaba katalizatora. Uporabom heterogenih katalizatora dobiva se kvalitetniji i čišći biodizel kao i glicerol, a zbog jednostavnijeg postupka i mogućnosti višestruke uporabe katalizatora danas se homogena kataliza sve više nastoji zamijeniti heterogenom.3,4,5 U posljednje vrijeme heterogeno katalizirana metanoliza vrlo se intenzivno istražuje. U različitim laboratorijskim istraživanjima heterogeno katalizirane metanolize upotrebljavan je velik broj različitih spojeva u funkciji katalizatora.6 Pri tome je mnogo pozornosti posvećeno istraživanju vrste, načina pripreme i količine heterogenog katalizatora, kao i uvjetima pri kojima se izvodi reakcija metanolize. Katalitička aktivnost heterogenih katalizatora ovisi o mnogo čimbenika, prije svega o njihovoj prirodi, veličini i specifičnoj površini čestica te primijenjenim uvjetima u kojima se reakcija izvodi.7 Između objavljenih rezultata ovih istraživanja postoje razlike oko optimalnih uvjeta procesa, pa čak i oko postojanja katalitičke aktivnosti nekih spojeva. Najveći broj istraživanja heterogeno katalizirane metanolize odnosi se na primjenu zemnoalkalijskih metala, točnije njihovih oksida kao katalizatora reakcije.3 Katalitička aktivnost oksida zemnoalkalijskih metala raste s povećanjem njihove bazičnosti i to redoslijedom;

The metal content (iron and copper) was potentiometrically analyzed in 44 tea samples. The analyzed samples included chamomile ( Matricaria chamomilla ), green tea ( Camellia sinensis ), sage tea ( Salvia officinalis L.), linden ( Tilia L.) and mint ( Mentha piperita ) in tea bags and bulk purchased at local supermarkets and marketplaces in Split, Croatia. Tea samples digestion was performed in microwave oven by using nitric acid and hydrogen peroxide mixture. Potentiometric determination was performed by using FISE for Fe 3+ and CuISE for Cu 2+ , respectively, by using potentiometric methods previously developed in our laboratory. The measured results were compared with atomic absorption spectrometric measurements from our previous research and showed notable statistical superposition.