Aiming to address the issue of low accuracy in model predictions obtained from fitting frequency domain response curves for small unmanned helicopters during the process of modeling their flight dynamics, this study proposes a system identification algorithm based on the combination of weighted least squares and improved grey wolf optimisation algorithm. The algorithm utilises the weighted least squares method to obtain the initial model structure, optimises the initial model parameters using the improved grey wolf optimisation algorithm, and enhances the local search and global optimisation ability of the grey wolf optimisation algorithm by introducing an improved grey wolf subgrouping rule, nonlinear convergence factor and dynamic cooperative rule. Ultimately, this approach establishes a dynamic model for small, unmanned helicopters. The identified model is validated using flight test data, with findings demonstrating that this method achieves higher accuracy in model identification and better fits to frequency domain response curves, thus providing a more accurate reflection of the flight dynamics of small unmanned helicopters.

Let $\mathbb{N}$ be the set of all non-negative integers. For any integer r and m, let $r+m\mathbb{N}=\{r+mk: k\in\mathbb{N}\}$. For $S\subseteq \mathbb{N}$ and $n\in \mathbb{N}$, let $R_{S}(n)$ denote the number of solutions of the equation $n=s+s'$ with $s, s'\in S$ and $s \lt s'$. Let $r_{1}, r_{2}, m$ be integers with $0 \lt r_{1} \lt r_{2} \lt m$ and $2\mid r_{1}$. In this paper, we prove that there exist two sets C and D with $C\cup D=\mathbb{N}$ and $C\cap D=(r_{1}+m\mathbb{N})\cup (r_{2}+m\mathbb{N})$ such that $R_{C}(n)=R_{D}(n)$ for all $n\in\mathbb{N}$ if and only if there exists a positive integer l such that $r_{1}=2^{2l+1}-2, r_{2}=2^{2l+1}-1, m=2^{2l+2}-2$.

We study a growth model with two types of agents who are heterogeneous in their degree of family altruism. We prove that every equilibrium path of consumption, bequests, and capital converges to a unique steady state and study the effect of altruism on the properties of steady-state equilibrium. We show that aggregate income is positively related to both level of altruism and altruism heterogeneity. When altruism heterogeneity is low or moderate, income inequality follows an inverse U-shaped pattern relative to the level of altruism. These observations are consistent with the cross-country Kuznets curve linking different steady-state levels of income to steady-state levels of inequality. When altruism heterogeneity is high, income inequality decreases with the level of altruism. Our results suggest that heterogeneous altruism is a possible mechanism linking economic growth and income inequality.

A novel microstrip filtering antenna with slot coupling feed is presented in this work. An asymmetric interdigital coupling structure is used for the feed to excite the patch antenna through gap-fed coupling. Introducing a U-shaped slot on the patch surface modifies the current path to attain different resonant modes. The asymmetric coupled fingers in the low-frequency band generate a radiation null of −64 dBi, while additional resonances introduced in the high band broaden the bandwidth from 4.9 to 5.3 GHz. A horizontally shorted microstrip branch produces another null point of −28 dBi between the bands, enabling steeper roll-off and further improvement in frequency selectivity. The proposed filtering antenna provides a flexible filter response without requiring extra filtering circuits, with appreciable peak gains (6.1 dBi and 7.1 dBi) and stable radiation characteristics. This makes it suitable for WLAN (Wireless Local Area Network) and ISM (Industrial Scientific Medical) systems applications.

Let Γ be a finite graph and let $A(\Gamma)$ be the corresponding right-angled Artin group. From an arbitrary basis $\mathcal B$ of $H^1(A(\Gamma),\mathbb F)$ over an arbitrary field, we construct a natural graph $\Gamma_{\mathcal B}$ from the cup product, called the cohomology basis graph. We show that $\Gamma_{\mathcal B}$ always contains Γ as a subgraph. This provides an effective way to reconstruct the defining graph Γ from the cohomology of $A(\Gamma)$, to characterize the planarity of the defining graph from the algebra of $A(\Gamma)$ and to recover many other natural graph-theoretic invariants. We also investigate the behaviour of the cohomology basis graph under passage to elementary subminors and show that it is not well-behaved under edge contraction.

How closely related are modern anti-democratic beliefs among white Americans, and to what extent are these beliefs shaped by exclusionary racial attitudes? Using data from the Political Unrest Study, the Collaborative Multiracial Post-Election Survey (CMPS), Democracy Fund + UCLA Nationscape, and the Survey of the Performance of American Elections (SPAE), we find that support for voting restrictions, opposition to voting expansions, belief in widespread voter fraud, and support for overturning democratic election results load onto a single underlying dimension. While the prevalence of anti-democratic beliefs among white Americans has remained stable over the past decade, these beliefs have become increasingly interconnected. Furthermore, racial attitudes towards out-groups—including racial resentment, anti-immigrant sentiment, and white racial grievance—strongly correlate with anti-democratic beliefs, whereas in-group racial attitudes do not. Analysis of multiple waves of the American National Election Studies (ANES) reveals that racial resentment and white grievance now explain twice as much variation in anti-democratic beliefs as they did in 2012. Experimental evidence also demonstrates that white Americans react negatively to voting expansions when the racial implications of these reforms are made explicit. These findings underscore the growing alignment between anti-democratic beliefs and racial attitudes in contemporary U.S. politics.

Five discrete bismuth telluride compositions, characterised by high and variable degrees of Pb and Se substitutions, were observed at the Stall Lake VMS deposit in the Snow Lake area, Canada. The major cation substitutions are Pb (3.0 to 11.0 wt.%), Fe (0.2 to 1.4 wt.%), Cu (up to 0.9 wt.%) and Ag (up to 3.2 wt.%). The main anion substitution is Se (0.3 to 7.9 wt.%); S never exceeds 0.3 wt.%. These results were compared to a literature data compilation of all publicly available data for the pure bismuth tellurides tsumoite and tellurobismuthite, and the Pb-bearing rucklidgeite and kochkarite. On the basis of these new data and the literature compilation, a few generalisations about the substitutions in bismuth tellurides can be made. The major conclusion is that bismuth tellurides always contain at least some substitutional cations (Pb, Ag, Fe, Cu, Sb and Au), typically combining to ∼2 wt.% if Pb is excluded, and anions (mostly Se and some S, typically <1 wt.% combined). Another conclusion is that bismuth tellurides have highly variable compositions, which can be quite far from their theoretical ones, to the point of defining specific mineral varieties such as high-Pb tsumoite, low-Pb kochkarite, and high-Se rucklidgeite. Two high-Se bismuth telluride compositions were observed at Stall Lake (average Se ≈ 4.9 and ≈ 7.2 wt.%), which had never been documented before. This observation, in conjunction with the bismuth tellurides literature data, emphasises the high potential for both cation and anion substitutions in these minerals.

We compute primes $p \equiv 5 \bmod 8$ up to $10^{11}$ for which the Pellian equation $x^2-py^2=-4$ has no solutions in odd integers; these are the members of sequence A130229 in the Online Encyclopedia of Integer Sequences. We find that the number of such primes $p\leqslant x$ is well approximated by

$$ \begin{align*}\frac{1}{12}\pi(x) - 0.037\int_2^x \frac{dt}{t^{1/6}\log t},\end{align*} $$

where $\pi (x)$ is the usual prime counting function. The second term shows a surprising bias away from membership of this sequence.

We consider interacting urns on a finite directed network, where both sampling and reinforcement processes depend on the nodes of the network. This extends previous research by incorporating node-dependent sampling and reinforcement. We classify the sampling and reinforcement schemes, as well as the networks on which the proportion of balls of either colour in each urn converges almost surely to a deterministic limit. We also investigate conditions for achieving synchronisation of the colour proportions across the urns and analyse fluctuations under specific conditions on the reinforcement scheme and network structure.

We prove structural results for measure-preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions, these systems always have rational discrete spectrum and, as a consequence, zero entropy. We obtain several other refined structural and spectral results, one consequence of which is that the Archimedean characters are the only pretentious multiplicative functions that have Furstenberg systems with trivial rational spectrum, another is that a pretentious multiplicative function has ergodic Furstenberg systems if and only if it pretends to be a Dirichlet character, and a last one is that for any fixed pretentious multiplicative function, all its Furstenberg systems are isomorphic. We also study structural properties of Furstenberg systems of a class of multiplicative functions, introduced by Matomäki, Radziwiłł, and Tao, which lie in the intermediate zone between pretentiousness and strong aperiodicity. In a work of the last two authors and Gomilko, several examples of this class with exotic ergodic behavior were identified, and here we complement this study and discover some new unexpected phenomena. Lastly, we prove that Furstenberg systems of general bounded multiplicative functions have divisible spectrum. When these systems are obtained using logarithmic averages, we show that a trivial rational spectrum implies a strong dilation invariance property, called strong stationarity, but, quite surprisingly, this property fails when the systems are obtained using Cesàro averages.

This article offers the first detailed study of a manuscript preserving notes from the Modern Greek course held in 1801-2 by Jean-Baptiste-Gaspard d'Ansse de Villoison in Paris. The notebook was kept by Karl Benedikt Hase, later Professor of Modern Greek at the French École de langues orientales vivantes, during his attendance of Villoison's course as a student. The article sketches first the historical context of the notebook, before an analysis of its contents, and finally a comparison with Hase's later published work on the primary text at its core, Amiras’ Greek translation of Costin's History of Moldavia.