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We show that for every rational number $r \in (1,2)$ of the form $2 - a/b$, where $a, b \in \mathbb{N}^+$ satisfy $\lfloor b/a \rfloor^3 \le a \le b / (\lfloor b/a \rfloor +1) + 1$, there exists a graph $F_r$ such that the Tur\'an number $\operatorname{ex}(n, F_r) = \Theta(n^r)$. Our result in particular generates infinitely many new Tur\'an exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh--Conlon conjecture., Comment: 23 pages, 5 figures, published in Annals of Applied Mathematics

Acanthochitona rubrolineatus (Lischke, 1873) (Polyplacophora, Neoloricata, Cryptoplacidae) is an important species widely distributed in the middle and low tide zone of coastal intertidal zone along the China Sea coast. In recent years, the serious pollution of seawater has caused a sharp decline in the number of wild populations of A. rubrolineatus. Lacking of effective molecular markers limits the effective protection and management of this species. Studies for the isolation and characterization of 135 A. rubrolineatus SNPs markers were carried out. The frequency of minor allele ranges from 0.0125 to 0.5000. The observed heterozygosity and expected heterozygosity are 0.0000-0.9750, 0.0731-0.6696, respectively. The inbreeding value varies from -0.2902 to 0.9966. Among them, there are 27 sites markablely differently from Hardy-Weinberg equilibrium (P < 0.05). The study of the polymorphic SNPs will provide a therotical basis for further analysis of population genetic analysis on A. rubrolineatus.

The increasing demand for customized products and rapid prototyping triggers the development of dieless forming process where the need of part-specific dies is eliminated compared to conventional forming processes. This paper presents a heat-assisted three-roll incremental rolling system capable of producing rods and tubes of various diameters without the need for die/tool replacement. The system incorporates two possible heating mechanisms, namely, an induction heater and a high-current power supply for electrically assisted forming. Due to its high flexibility and hot forming ability, this rolling system is ideal for low volume production or scientific research. The newly fabricated rolling machine was initially evaluated using low carbon steel rods. The experiments have shown that the machine can produce metallic rods down to 6 mm in diameter without apparent spiral marks on the outer surface of the rolled product using multiple passes. The finite element method (FEM) was used to analyze the reaction moment, depth of the spiral marks, and the effect of axial feeding speed on the spiral marks. The simulation model predicted the results of the experiments with less than a 10% error. The work established a flexible rolling platform for possible future research, which can include the study of interface behavior in the thermo-mechanical rolling processes, and the study of material behavior in this multi-axial multi-physics environment.

Incremental sheet forming (ISF) offers great flexibility in producing complex sheet parts as compared with conventional sheet forming processes where part-specific die sets are required to form a product. While there are many potential applications of ISF in various industries, toolpath planning for multifeature parts remains a leading challenge hindering the wide adoption of ISF. In this study, a criterion based on the gradient of the target surface was established for determining the appropriate feature forming sequence. Based on the analysis of the gradients of the surface, multifeature geometries were separated into two categories: “plane-referenced” and “surface-referenced.” Experimental investigations of forming a multifeature air intake as an example were carried out to demonstrate the proposed criterion and feature forming sequence. The results show that the choice of the optimal sequence depends on the type of geometry formed. The proposed criterion extends existing toolpath strategies for relatively regular geometries, where features are formed from flat or inclined bases to more complex geometries with features on a curved basis. This work will be of interest to both design and manufacturing communities.

A Ru-catalyzed meta-selective C-H nitration of 2-arylbenzothiazoles and 2-arylthiazoles has been developed. A wide range of functional groups are tolerated, providing the meta-nitrated products in good to excellent yields using Cu(NO3)2·3H2O as the nitro source. The nitration could be carried out on a gram scale and used for the synthesis of promising therapeutic leads for human African trypanosomiasis.

In this study, we investigated the use of an electrically-assisted (EA) forming process to reduce the forming force of ODS ferritic steels. The effects of a continuous electric current on 14YWT, which is a kind of ODS material, during plastic deformation were evaluated. First, EA uniaxial tension tests show that the electric current is able to reduce the flow stress of 14YWT. 14YWT exhibits a ductility minimum at a current density of 34.5 A/mm2 which is consistent with fractography results. Hardness measurements and TEM results indicate that oxide particles are stable during the EA process. Second, microstructure analysis was performed on the sample in its as-received state and after current treatment. The microstructures are stable when subjected to high current density. Third, a thermal model was developed to predict the Joule heating temperatures. The temperatures were compared with the experimental results. Finally, a temperature-dependent hardening model was used to explore the mechanisms acting during EA deformation. Since the model can accurately predict the yield strength of 14YWT under EA conditions without the incorporation of non-thermal effects, it can be concluded that the reduction in yield strength is due to the Joule heating generated under continuous current loading conditions. An oven-heated pure thermal tension test was conducted to confirm this conclusion. The findings generated from this study will result in the development of innovative manufacturing processes such as the electrically-assisted tube forming processes.

We determine the exact value of the optimal symmetric rate point $(r, r)$ in the Dueck zero-error capacity region of the binary adder channel with complete feedback. We proved that the average zero-error capacity $r = h(1/2-\delta) \approx 0.78974$, where $h(\cdot)$ is the binary entropy function and $\delta = 1/(2\log_2(2+\sqrt3))$. Our motivation is a problem in quantitative group testing. Given a set of $n$ elements two of which are defective, the quantitative group testing problem asks for the identification of these two defectives through a series of tests. Each test gives the number of defectives contained in the tested subset, and the outcomes of previous tests are assumed known at the time of designing the current test. We establish that the minimum number of tests is asymptotic to $(\log_2 n) / r$ as $n \to \infty$., Comment: 39 pages, 3 figures, accepted to IEEE Trans. Inf. Theory, corrections suggested by the referees have been incorporated

Given a system $(G_1, \ldots ,G_m)$ of graphs on the same vertex set $V$, a cooperative coloring is a choice of vertex sets $I_1, \ldots ,I_m$, such that $I_j$ is independent in $G_j$ and $\bigcup_{j=1}^{m}I_j = V$. For a class $\mathcal{G}$ of graphs, let $m_{\mathcal{G}}(d)$ be the minimal $m$ such that every $m$ graphs from $\mathcal{G}$ with maximum degree $d$ have a cooperative coloring. We prove that $\Omega(\log\log d) \le m_\mathcal{T}(d) \le O(\log d)$ and $\Omega(\log d)\le m_\mathcal{B}(d) \le O(d/\log d)$, where $\mathcal{T}$ is the class of trees and $\mathcal{B}$ is the class of bipartite graphs., Comment: 8 pages, 2 figures, accepted to the Electronic Journal of Combinatorics, corrections suggested by the referees have been incorporated

Let $\mathbb{P}^s$ be the $s$-dimensional complex projective space, and let $X, Y$ be two non-empty open subsets of $\mathbb{P}^s$ in the Zariski topology. A hypersurface $H$ in $\mathbb{P}^s\times\mathbb{P}^s$ induces a bipartite graph $G$ as follows: the partite sets of $G$ are $X$ and $Y$, and the edge set is defined by $\overline{u}\sim\overline{v}$ if and only if $(\overline{u},\overline{v})\in H$. Motivated by the Tur\'an problem for bipartite graphs, we say that $H\cap (X\times Y)$ is $(s,t)$-grid-free provided that $G$ contains no complete bipartite subgraph that has $s$ vertices in $X$ and $t$ vertices in $Y$. We conjecture that every $(s,t)$-grid-free hypersurface is equivalent, in a suitable sense, to a hypersurface whose degree in $\overline{y}$ is bounded by a constant $d = d(s,t)$, and we discuss possible notions of the equivalence. We establish the result that if $H\cap(X\times \mathbb{P}^2)$ is $(2,2)$-grid-free, then there exists $F\in \mathbb{C}[\overline{x},\overline{y}]$ of degree $\le 2$ in $\overline{y}$ such that $H\cap(X\times \mathbb{P}^2) = \{F = 0\}\cap (X\times \mathbb{P}^2)$. Finally, we transfer the result to algebraically closed fields of large characteristic., Comment: 13 pages, accepted to Discrete Math., corrections suggested by the referees have been incorporated

A zone of width $\omega$ on the unit sphere is the set of points within spherical distance $\omega/2$ of a given great circle. We show that the total width of any collection of zones covering the unit sphere is at least $\pi$, answering a question of Fejes T\'oth from 1973., Comment: 10 pages, 3 figures, this version adds some conjectures, accepted to Geom. Funct. Anal., corrections suggested by the referees have been incorporated

A Ru-catalyzed

Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. Fix $0 < \alpha < 1$. Let $N_\alpha(d)$ denote the maximum number of lines through the origin in $\mathbb{R}^d$ with pairwise common angle $\arccos \alpha$. Let $k$ denote the minimum number (if it exists) of vertices in a graph whose adjacency matrix has spectral radius exactly $(1-\alpha)/(2\alpha)$. If $k < \infty$, then $N_\alpha(d) = \lfloor k(d-1)/(k-1) \rfloor$ for all sufficiently large $d$, and otherwise $N_\alpha(d) = d + o(d)$. In particular, $N_{1/(2k-1)}(d) = \lfloor k(d-1)/(k-1) \rfloor$ for every integer $k\ge 2$ and all sufficiently large $d$. A key ingredient is a new result in spectral graph theory: the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity., Comment: 11 pages. Fixed a minor issue at the end of the proof of Theorem 1.2

Electricity in many countries such as the US and China is produced by burning fossil fuels in steam-turbine-driven power plants. The efficiency of these power plants can be improved by increasing the operating temperature of the steam generator. In this work, we adopted a combined surface science and computational thermodynamics approach to the design of high-temperature, corrosion-resistant steels for this application. The result is a low-carbon ferritic steel with nanosized transition metal monocarbide precipitates that are thermally stable, as verified by atom probe tomography. High-temperature Vickers hardness measurements demonstrated that these steels maintain their strength for extended periods at 700 °C. We hypothesize that the improved strength of these steels is derived from the semi-coherent interfaces of these thermally stable, nanosized precipitates exerting drag forces on impinging dislocations, thus maintaining strength at elevated temperatures.

As one of the promising micro-manufacturing technologies, micro-forming has economical and ecological advantages in terms of mass and near-net-shape production. However, size effects increasingly affect material performances with scaling down geometry and process parameters and consequently hinder applications of micro-forming. Electrically-assisted (EA) micro-forming may have the potential to minimize the size effects. In order to investigate the size effects in the EA micro-forming, uniaxial tension tests were conducted on miniaturized AZ31 tensile samples with varying grain sizes and geometry sizes at a constant DC current density. It was found that the normalized flow stress reduction, i.e., decreases of flow stresses/flow stresses at room temperature (RT), increased with the decrease of the grain size and with the increase of the geometry size at the constant current density of 91.1 A/mm2. Additionally, tests for the isolation of bulk Joule heating such as oven-heated tests and air-cooled EA tests were also conducted on the smallest samples with the same grain size regime examined in the EA tests to comparatively analyze the effect of grain size on the flow stress behavior during EA micro-tension. It was found that the amount of the Hall-Petch slope decreases in order of the RT, the oven-heated and the EA micro-tension tests. Both the Hall-Petch effects in the EA tests and the air-cooled EA tests are insignificant, showing nearly levelled Hall-Petch curves across the grain size regime examined. Based on these observations, a composite material model taking account of localized Joule heating at grain boundaries was developed to qualitatively interpret the Hall-Petch slope differences in the above four conditions. It was found that the mechanism behind the effects due to electric current may not be exclusive to bulk thermal softening.

This experimental work demonstrates a new cost-effective way of achieving superhydrophobicity on metallic surfaces by micro-texturing with a novel water jet guided laser process. Compared to conventional pure laser texturing by nanosecond, picosecond and femtosecond lasers, water jet guided laser processing yields textures with an almost zero heat affected zone while the debris on the textured surface is simultaneously cleaned by the jet during the process. The effects of grid spacing, laser power coupled into the jet and water jet diameter are examined and processing conditions for achieving superhydrophobicity are provided. Changes in the wetting of the surface over time under ambient conditions from hydrophilic to superhydrophobic, due to changes in surface chemistry, were explored. It has been shown that the surface contact angle dramatically increases within the first couple of days after texturing when exposed to air. After around 20 days, the contact angle stabilized at 150°, 130° and 129° on textured 304 stainless steel, titanium and 6061 aluminum surfaces, respectively.

We prove a vertex isoperimetric inequality for the $n$-dimensional Hamming ball $\mathcal{B}_n(R)$ of radius $R$. The isoperimetric inequality is sharp up to a constant factor for sets that are comparable to $\mathcal{B}_n(R)$ in size. A key step in the proof is a local expansion phenomenon in hypercubes., 19 pages, 1 figure, published in the Electronic Journal of Combinatorics

The exact values of the optimal symmetric rate point in the Cover--Leung capacity region of the two-user union channel with complete feedback were determined by Willems when the size of the input alphabet is 2, and by Vinck, Hoeks and Post when the size is at least 6. We complete this line of research when the size of the input alphabet is 3, 4 or 5. The proof hinges on the technical lemma that concerns the maximal joint entropy of two independent random variables in terms of their probability of equality. For the zero-error capacity region, using superposition coding, we provide a practical near-optimal communication scheme which improves all the previous explicit constructions., 16 pages, 1 figure, 1 table, accepted to IEEE Trans. Inf. Theory, corrections suggested by the referees have been incorporated

We study several problems in discrete geometry and extremal combinatorics. Discrete geometry studies the combinatorial properties of finite sets of simple geometric objects. One theme of the field is geometric Ramsey theory. Given m geometric objects, we want to select a not too small subset forming a configuration that is “regular” in some sense.

Given two disjoint convex polyhedra, we look for a best approximation pair relative to them, i.e., a pair of points, one in each polyhedron, attaining the minimum distance between the sets. Cheney and Goldstein showed that alternating projections onto the two sets, starting from an arbitrary point, generate a sequence whose two interlaced subsequences converge to a best approximation pair. We propose a process based on projections onto the half-spaces defining the two polyhedra, which are more negotiable than projections on the polyhedra themselves. A central component in the proposed process is the Halpern--Lions--Wittmann--Bauschke algorithm for approaching the projection of a given point onto a convex set., 14 pages, 8 figures, accepted to Computational Optimization and Applications (COAP)

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Let $\mathcal{F}(\lambda)$ be the family of connected graphs of spectral radius $\le \lambda$. We show that $\mathcal{F}(\lambda)$ can be defined by a finite set of forbidden subgraphs if and only if $\lambda < \lambda^* := \sqrt{2+\sqrt{5}} \approx 2.058$ and $\lambda \not\in \{\alpha_2, \alpha_3, \dots\}$, where $\alpha_m = \beta_m^{1/2} + \beta_m^{-1/2}$ and $\beta_m$ is the largest root of $x^{m+1}=1+x+\dots+x^{m-1}$. The study of forbidden subgraphs characterization for $\mathcal{F}(\lambda)$ is motivated by the problem of estimating the maximum cardinality of equiangular lines in the $n$-dimensional Euclidean space $\mathbb{R}^n$ --- a family of lines through the origin such that the angle between any pair of them is the same. Denote by $N_\alpha(n)$ the maximum number of equiangular lines in $\mathbb{R}^n$ with angle $\arccos\alpha$. We establish the asymptotic formula $N_\alpha(n) = c_\alpha n + O_\alpha(1)$ for every $\alpha \ge \frac{1}{1+2\lambda^*}$. In particular, $N_{1/3}(n) = 2n+O(1)$ and $N_{1/5}(n), N_{1/(1+2\sqrt{2})}(n) = \frac{3}{2}n+O(1)$. Besides we show that $N_\alpha(n) \le 1.49n + O_\alpha(1)$ for every $\alpha \neq \tfrac{1}{3}, \tfrac{1}{5}, \tfrac{1}{1+2\sqrt{2}}$, which improves a recent result of Balla, Dr\"axler, Keevash and Sudakov., Comment: 23 pages, this version fixes an error in Theorem 1, accepted to Israel J. Math., corrections suggested by the referee have been incorporated

Given a graph $G$, the unraveled ball of radius $r$ centered at a vertex $v$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$. We prove a lower bound on the maximum spectral radius of unraveled balls of fixed radius, and we show, among other things, that if the average degree of $G$ after deleting any ball of radius $r$ is at least $d$ then its second largest eigenvalue is at least $2\sqrt{d-1}\cos(\frac{\pi}{r+1})$., Comment: 8 pages, accepted to J. Comb. Theory B, corrections suggested by the referees have been incorporated

A grid generation method for the three-dimensional arbitrary complex geometry of casting is introduced for the foundry simulation. The approach of a STL (STereo Lithography) model from CAD to a distance field is described in detail. The mesh generated by this approach is based on a fully threaded tree and refined at specific positions according to the distance field. This algorithm may make the mesh become fine at the surface and coarse inside. Several examples are provided to validate this algorithm.

Due to a calculation error, the constant in the main theorem is not $80 \sqrt{k\log k}$ but $80\sqrt{k} \log k$. The error was discovered by Xizhi Liu.For a new discussion on the limit of the method used in this paper see the revised arXiv version of the paper.

We show that, for each fixed $k$, an $n$-vertex graph not containing a cycle of length $2k$ has at most $80\sqrt{k}\log k\cdot n^{1+1/k}+O(n)$ edges., Comment: 16 pages, v2 appeared in Comb. Probab. Comp., v3 fixes an error in v2 and explains why the method in the paper cannot improve the power of k further, v4 fixes the proof of Theorem 12 introduced in v3