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The process of wood debarking plays a crucial role in determining the price and quality of the final product. Hence, this work aims to elaborate on a theoretical basis for upgrading wood chips production technology. Consideration should be given to the influence of various debarking parameters when processing wood in barking drums. Such parameters as the number of wood collisions with each other and against a drum body, shear pressure, and others were chosen as equation coefficients to model the wood debarking time and knife sharpening angle. The treatment time is shown to depend on the number of collisions, the diameter of the log and indices that consider filling, the proportion of bark and the thickness, and wood hardness. It was established that the time required to debark the tree using knives is 1.5-3 times lower depending on the temperature of raw materials. Moreover, the process tends to be intensified with increasing knife sharpness.

Thinning is a necessary and complex forestry activity. The complexity increases due to theoretical disagreements, contradictory recommendations, and errors of modern practice, which require confirmation through long-time experiments. This article presents a summary of experimental results from plantations established 20–30 years ago and explains concepts of the theory, methods, and regime of thinning in permanent sample plots of pine stands in Gatchinsky forest of the Leningrad region. The research results allow for the clarification of growth patterns and age dynamics of pine stands subject to heavy, low thinning, as well as the results of applying the crown (high) thinning technique and a mixed treatment. A combined thinning and fertilization could improve wood quality and yield compared to conventional methods. Of particular scientific importance is the analysis of change in tree diameter classes during growth and after thinning. The research results allow for optimizing the treatment regime in pine plantations and reducing labor intensity by increasing the intensity of thinning and reducing the number of techniques.

A graph G arrows a graph H if in every 2-edge-colouring of G there exists a monochromatic copy of H. Schelp had the idea that if the complete graph $K_n$ arrows a small graph H, then every ‘dense’ subgraph of $K_n$ also arrows H, and he outlined some problems in this direction. Our main result is in this spirit. We prove that for every sufficiently large n, if $n = 3t+r$ where $r \in \{0,1,2\}$ and G is an n-vertex graph with $\delta(G) \ge (3n-1)/4$ , then for every 2-edge-colouring of G, either there are cycles of every length $\{3, 4, 5, \dots, 2t+r\}$ of the same colour, or there are cycles of every even length $\{4, 6, 8, \dots, 2t+2\}$ of the samecolour.Our result is tight in the sense that no longer cycles (of length $>2t+r$ ) can be guaranteed and the minimum degree condition cannot be reduced. It also implies the conjecture of Schelp that for every sufficiently large n, every $(3t-1)$ -vertex graph G with minimum degree larger than $3|V(G)|/4$ arrows the path $P_{2n}$ with 2n vertices. Moreover, it implies for sufficiently large n the conjecture by Benevides, Łuczak, Scott, Skokan and White that for $n=3t+r$ where $r \in \{0,1,2\}$ and every n-vertex graph G with $\delta(G) \ge 3n/4$ , in each 2-edge-colouring of G there exists a monochromatic cycle of length at least $2t+r$ .

The Erd\H{o}s-Simonovits stability theorem states that for all \epsilon >0 there exists \alpha >0 such that if G is a K_{r+1}-free graph on n vertices with e(G) > ex(n,K_{r+1}) - \alpha n^2, then one can remove \epsilon n^2 edges from G to obtain an r-partite graph. F\"uredi gave a short proof that one can choose \alpha=\epsilon. We give a bound for the relationship of \alpha and \varepsilon which is asymptotically sharp as \epsilon \to 0., Comment: 12 pages, 1 figure

This study investigates the problem of vehicle exploitation in the mountainous and wooded regions of the Russian Federation. Considering how critical rollover accidents are in the logging industry, it is vital to ensure safe and stable driving. This study aims to develop a model of electric power steering (EPS) control using a quasi-continuous sliding-mode controller in MATLAB/Simulink. Experiments were carried out under the following conditions: maximum slope angle, 30°; maximum steering angle, 30°; maximum driving speed, 7 m/s. The dynamic characteristics of the suspension and EPS systems were optimized using the receding horizon optimization technique. The theoretical and experimental results suggest that the model reaches its critical state of stability (−0.2) at a speed range of 0–7 m/s with a steering angle of 25°. After optimization, critical stability (0.3) occurs at the driving speed of 7 m/s when the steering angle is 30°. The paper discussed the possibility of installing the EPS control system into vehicles that operate in mountainous wooded areas.

A hypergraph $\mathcal H$ is super-pancyclic if for each $A \subseteq V(\mathcal H)$ with $|A| \geq 3$, $\mathcal H$ contains a Berge cycle with base vertex set $A$. We present two natural necessary conditions for a hypergraph to be super-pancyclic, and show that in several classes of hypergraphs these necessary conditions are also sufficient for this. In particular, they are sufficient for every hypergraph $\mathcal H$ with $ \delta(\mathcal H)\geq \max\{|V(\mathcal H)|, \frac{|E(\mathcal H)|+10}{4}\}$. We also consider super-cyclic bipartite graphs: those are $(X,Y)$-bigraphs $G$ such that for each $A \subseteq X$ with $|A| \geq 3$, $G$ has a cycle $C_A$ such that $V(C_A)\cap X=A$. Such graphs are incidence graphs of super-pancyclic hypergraphs, and our proofs use the language of such graphs., Comment: 17 pages

We solve four similar problems: For every fixed $s$ and large $n$, we describe all values of $n_1,\ldots,n_s$ such that for every $2$-edge-coloring of the complete $s$-partite graph $K_{n_1,\ldots,n_s}$ there exists a monochromatic (i) cycle $C_{2n}$ with $2n$ vertices, (ii) cycle $C_{\geq 2n}$ with at least $2n$ vertices, (iii) path $P_{2n}$ with $2n$ vertices, and (iv) path $P_{2n+1}$ with $2n+1$ vertices. This implies a generalization for large $n$ of the conjecture by Gy\'arf\'as, Ruszink\'o, S\'ark\H{o}zy and Szemer\'edi that for every $2$-edge-coloring of the complete $3$-partite graph $K_{n,n,n}$ there is a monochromatic path $P_{2n+1}$. An important tool is our recent stability theorem on monochromatic connected matchings., Comment: 46 pages, 4 figures

An $\epsilon$-distance-uniform graph is one in which from every vertex, all but an $\epsilon$-fraction of the remaining vertices are at some fixed distance $d$, called the critical distance. We consider the maximum possible value of $d$ in an $\epsilon$-distance-uniform graph with $n$ vertices. We show that for $\frac1n \le \epsilon \le \frac1{\log n}$, there exist $\epsilon$-distance-uniform graphs with critical distance $2^{\Omega(\frac{\log n}{\log \epsilon^{-1}})}$, disproving a conjecture of Alon et al. that $d$ can be at most logarithmic in $n$. We also show that our construction is best possible, in the sense that an upper bound on $d$ of the form $2^{O(\frac{\log n}{\log \epsilon^{-1}})}$ holds for all $\epsilon$ and $n$., Comment: 12 pages, 1 figure

Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of $G$ are colored. The game chromatic number \chi_g(G) is the minimum k for which the first player has a winning strategy. The paper \cite{BFS} began the analysis of the asymptotic behavior of this parameter for a random graph G_{n,p}. This paper provides some further analysis for graphs with constant average degree i.e. np=O(1) and for random regular graphs., Comment: Correction

For Legendrian links in the 1-jet space of $S^1$ we show that the 1-graded ruling polynomial may be recovered from the Kauffman skein module. For such links a generalization of the notion of normal ruling is introduced. We show that the existence of such a generalized normal ruling is equivalent to sharpness of the Kauffman polynomial estimate for the Thurston-Bennequin number as well as to the existence of an ungraded augmentation of the Chekanov-Eliashberg DGA. Parallel results involving the HOMFLY-PT polynomial and 2-graded generalized normal rulings are established., Comment: 26 pages, 6 figures

Human observers are able to identify a person based on his or her gait. However, little is known about the underlying mechanisms and the kind of information used to accomplish such a task. In this study, participants learned to discriminate seven male walkers shown as point-light displays from frontal, half-profile, or profile view. The displays were gradually normalized with respect to size, shape, and walking frequency, and identification performance was measured. All observers quickly learned to discriminate the walkers, but there was an overall advantage in favor of the frontal view. No effect of size normalization was found, but performance deteriorated when shape or walking frequency was normalized. Presenting the walkers from novel viewpoints resulted in a further decrease in performance. However, even after applying all normalization steps and rotating the walker by 90 degrees, recognition performance was still nearly three times higher than chance level.

In [On the HOMFLY-PT skein module of S1 × S2, Math. Z. 237(4) (2001) 769–814], Gilmer and Zhong established the existence of an invariant for links in S1 × S2 which is a rational function in variables a and s and satisfies the HOMFLY-PT skein relations. We give formulas for evaluating this invariant in terms of a standard, geometrically simple basis for the HOMFLY-PT skein module of the solid torus. This allows computation of the invariant for arbitrary links in S1 × S2 and shows that the invariant is in fact a Laurent polynomial in a and z = s – s-1. Our proof uses connections between HOMFLY-PT skein modules and invariants of Legendrian links. As a corollary, we extend HOMFLY-PT polynomial estimates for the Thurston–Bennequin number to Legendrian links in S1 × S2 with its tight contact structure.